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.. , .. , ..
- -
2015
Copyright & A K-C
517.968 (075.8)
22.161.675
39
.. , , ,
.. , ,
, . .
39 : - - / .. , .. , .. ; - . , . . . -. : , 2015. 104 .: .
517.968 (075.8)
22.161.675
.., .., .., 2015
. , 2015
Copyright & A K-C
3
................................................................................................................................................ 3
..................................................................................................................................................... 4
1 ......................................................................................... 7 1.1 ...................................................................................................................................... 7 1.2 ................................................................................................................................. 9 1.3 ........................ 12 1.4 ........................................................................................................................................................... 16 1.5. ................................... 19 1.6 - ................................................................................................................................................................ 25 1.7 (x,+) ................................................... 28 1.8 1- ......................................................................... 32
2 2- ............................................................................................. 35 2.1 ................................................................................................................................... 35 2.2 .................................................................................................. 38 2.3 ................................................ 42 2.4 .................................................................... 52 2.5 .............................................................. 57 2.6 , ......................................................................................................................................................... 64 2.7 ..................... 67 2.8 ................................................................................... 68
...... 77
.......................................................... 87
........................................................................ 89
........................................................................................ 104
Copyright & A K-C
4
1.
, , ,
,
()!
!
.
, , () , ..
()!
!
.
= (, )
( ! = (0, )) = , ( ! = 0
, .
(,)
, , ,
!()!
!
().
, !(, ) !.
!
1.
.
2. ! !.
Copyright & A K-C
5
3. () ! ,
() !
4. () ! () ! ,
()()!
!
!
!()!
!
! !
!
(1)
() ! () ! ,
,
, = .!
!
(2)
() !
= (, ) = !()!
!
(3)
5. !
+ + (4)
6. . () ! , ! , , ! ,
(, ).
! () ! = 0,!
!
, ! , ! ,
, , ().
!() ! (),
() ! !() () .
, !() !
, > 0 > 0,
! () ! ,!
!
Copyright & A K-C
6
> > .
. !()
, ,
. ! , ..
! ,
!.
() !(, )
(, ), () . ,
= (, ).
(, )
= , ,
! , < +!
!
.
(, )
= !(, )!
!
.
Copyright & A K-C
7
1
1.1
= + (, )()!
!
, (1.1)
(), (, ) , () ,
, 2-
. (, ) . () 0,
(1.1)
= (, )()!
!
, (1.2)
2- .
, = ()!
!
, (1.3)
, 1-
. , ,
.
(1.1), (1.2) (1.3)
, , ,
( ).
. ,
=1
1 + !!!
Copyright & A K-C
8
=1
1 + !+23
1 + !
()!
!
(1.4)
. () (1.4) !(!!!!)
! !,
11 + !
+
1 + !1
1 + ! ! !
!
!
=1
1 + !+23
1
1 + !32
1 + ! ! !!!!
!!!
=
=1
1 + !+
1
1 + ! ! !
11 + !
=1
1 + ! ! != .
, = !(!!!!)
! ! (1.4)
: 1
(1 + !)!!=
1
(1 + !)!!
, , = !(!!!!)
! !
(1.4).
,
.
1 =1
(1 + !)!!
, =3 + 2!
3 1 + ! !
3 + 2! 1 + ! !
!
!
.
2 = ! ! !sin! ,
= 1 !! cos 1 !! sin 1 + + 1 !! .!
!
3 = ! , = sin + 2 cos .!
!
Copyright & A K-C
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4 = !
6, = sh .
!
!
5 = 1 , !!! = .!
!
6 = 3, ! = ! .!
!
7 =12
, ()
= .!
!
8 =1
,
()
= 1!
!
1.2
!!
+ ! !!!!!!
++ ! = , (1.5)
! = 1,2, ,
0 = !, ! 0 = !,, !!! 0 = !!!, (1.6)
2- .
2-o
!!
+ ! + ! = , (1.5')
0 = !, ! 0 = !. (1.6')
!!
= . (1.7)
(1.6'), :
Copyright & A K-C
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= + !, = + ! + !
!
!
!
!
(1.8)
-
!
!!
!
!!
!
!!
=1
1 ! !!!
!
!!
(1.7) (1.8), (1.5') :
+ ! !
!
+ !! +
+ ! + !! + !! = ()!
!
+ ! + ! =!
!
= !! !! !!().
(1.9)
, = ! + ! , (1.10)
= !! !! !! . (1.11)
(1.9)
= , + ()!
!
, (1.12)
. . 2-ro .
(1.12)
(1.5') (1.6')
= 0.
, (1.12) ,
(1.10) (1.11), , ()
Copyright & A K-C
11
(1.8),
(1.5'), (1.6').
. ,
!! + ! + = 0 (1.13)
0 = 1, ! 0 = 0. (1.14)
.
!!
= . (1.15)
= + ! 0 = ,
!
!
!
!
= + 1!
!
. (1.16)
(1.15) (1.16) ,
+ + + 1 = 0,!
!
!
!
= 1 2 .!
!
,
:
9. !! + = 0; 0 = 0, ! 0 = 1.
10. ! = 0; 0 = 1.
11. !! + = cos ; 0 = ! 0 = 0.
12. !! 5 + 6 = 0; 0 = 0, ! 0 = 1.
Copyright & A K-C
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13. !! + = cos ; 0 = 0, ! 0 = 1.
14. !! ! !"# ! + ! = ; 0 = 1, ! 0 = 1.
15. !! + 1 + ! = cos ; 0 = 0, ! 0 = 2.
16.!!! + !! + ! = ! + 1; 0 = ! 0 = 1, !! 0 = 0.
17. !!! 2 = 0; 0 = !!, ! 0 = ! 0 = 1.
1.3
2-
= + , ,!
!
(1.17)
(, ) 0 , 0 ,
0 .
(l.17)
:
= ! + ! + !! ++ !! +. (1.18)
(1.17),
! + ! + !! ++ !! + =
= + , ! + ! ++ !! + .!
!
(1.19)
, :
! = ,
(1.20) ! = , ! = (, )()
!
!
!
!
,
Copyright & A K-C
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! = , ! = (, ) (, !)(!)!!
!
!
!
!
!
,
.
(1.20)
!(). ,
(, ) (1.18)
0,
(1.17).
, (1.20) :
! = , ,!
!
(1.21)
! = , , ! ! !
!
!
=!
!
= (!)! , , ! = ! , ! ! !,!
!
!
!!
!
!
(1.22)
! , ! = , , ! .!
!!
(1.23)
,
! = ! , , !
!
= 1,2, .
(1.24)
! ,
.
! , = , ,
!!! , = , ! , ,!
!
= 1,2, . (1.25)
Copyright & A K-C
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(1.24) (1.25), (1.18) :
= + ! ! , .!
!
!
!!!
(1.26)
, ; ,
, ; = !!
!!!
!!! , (1.27)
( )
(1.17). (1.27) ,
.
,
.
, ;
:
, ; = , + (, )(, ; )!
!
. (1.28)
(1.17)
= + (, ; )()!
!
(1.29)
.
(, ) 1.
. ! , = , = 1. , (1.25)
! , = , ! , = = ,!
!
!
!
! , = 1 =( )!
2
!
!
,
Copyright & A K-C
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! , = 1 !
2 =
!
3!,
!
!
.
! , = 1 !!! , = 1 !!!
2 ! =
( )!!!
1 !
!
!
!
!
.
,
, ; = !!!! , =!( )!
!= !(!!!).
!
!!!
!
!!!
:
:
36 = ! + !!!()!
!
37 = sin + 2 !!!()!
!
19 , =
20 , = !!!
21 , = !!!!!
22 , =1 + !
1 + !
23 , =2 + cos2 + cos
24 , =chch
25 , = !!!, > 0
Copyright & A K-C
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38 = 3! 3!!!()!
!
39 = ! +2 + cos2 + cos
()!
!
40 = 1 2 !!!!!()!
!
41 = !!!!! + 2 !!!!!()!
!
42 = 1 + ! +1 + !
1 + !()
!
!
43 =1
1 + !+ sin ( )()
!
!
44 = !!
! + ! !!! ()!
!
45 = !! + ! !!! sin !
!
()
1.4
2-
= + , .!
!
(1.30)
, 0, , ,
0 , 0 .
Copyright & A K-C
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- 0, ! .
(1.30) ! ,
! = + (, )!()!
!
.
!
0, . ,
! , ! , , ! ,,
! = + , !!! .!
!
,
{! ()} ()
(1.29).
, , !() , ! ()
(1.19) . 1.3,
(1.30).
!() {! ()}
.
.
= 1 + ,!
!
! 0.
. ! 0, ! = 1. ,
! = 1 + 1 !
!
= 1 + ,
! = 1 + 1 + !
!
= 1 + +!
2,
Copyright & A K-C
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! = 1 + 1 + +!
2 =
!
!
1 + +!
2!+!
3!.
,
! = 1 +1!+!
2!++
!!!
1 !.
, ! n-
!
!= !
!
!!!
.
, !() !.
, = !
,
! = 1 + !,!
!
! = 1 + ! !!!!!! = 1 + ! !,
! = ! .
:
46 = , !() 0.!
!
47 = 1 + , ! = 1.!
!
48 = 1 ,! 0.!
!
49 = + 1 ,!
!
a) ! = 1, ) ! = + 1.
Copyright & A K-C
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50 =!
2+ ,
!
!
a) ! = 1, ) ! = ,
) ! =!!
!+ .
51 = 1 + + , ! = 1.!
!
52 = 2 + 2 ,!
!
a) ! = 1, ) ! = 2.
53 = 2! + 2 ,!
!
) ! = 2, ) ! = 2.
54 =!
3 2 , ! = !.
!
!
55. ,
! , < +.!
!
!
!
,
, = 0!
!
() 0 ! 0, .
1.5.
! !() ,
0. !(),
! = ! ! .!
!
(1.31)
Copyright & A K-C
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, 0 ,
. ! !() -
,
! = ! !, (1.32)
..
( ).
2-
= + ,!
!
(1.33)
.
(1.33) .
,
,
() !!!! , !!!! (1.34)
, ,
() (1.34):
() !!!! .
, ,
() ,
Re = > max(!, !, !).
, , .
(1.33)
,
= + . (1.35)
=()
1 () 1 .
Copyright & A K-C
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()
(1.33).
.
= sin + 2 cos .!
!
. ,
sin 1
! + 1, cos
! + 1
.
.
( ),
=1
! + 1+
2! + 1
.
1 2
! + 1=
1! + 1
=1
( 1)! ! .
,
= ! .
:
59 = ! !!! .!
!
60 = !!! .!
!
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61 = !! + !!! .!
!
62 = .!
!
63 = cos ( ) cos .!
!
64 = 1 + + !! !!! .!
!
65 = + sin .!
!
66 = sin + .!
!
67 = sh .!
!
68 = 1 2 4! + 3 6 4 ! .!
!
69 = sh ch .!
!
70 = 1 + 2 cos .!
!
71 = ! + 2 cos .!
!
72 = cos + .!
!
Copyright & A K-C
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! = ! + !" ! = 1, 2, , , !
!
!
!!!
(1.36)
!" , !() ,
.
(1.36) ,
! = ! + !" ! ,!
!!!
( = 1, 2, , ) (1.37)
!().
, !(),
(1.36).
.
! = 1 2 ! !!! ! + ! ,!
!
!
!
! = 4 ! + 4 ! .!
!
!
!
(1.38)
.
,
! =1
2 2
! +1! ,
! =4!1! +
4!! .
!() !(),
! =
( + 1)!=
1 + 1
1
( + 1)!
! =3 + 2
( 2)( + 1)!=89
1
2+13
1
+ 1 !89
1
+ 1.
!() !()
Copyright & A K-C
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! = !! !!
! =89!! +
13!!
89!!
! ,!()
(1.38).
:
73
! = sin + ! ,!
!
! = 1 cos !()!
!
74
! = !! + ! ,!
!
! = 1 ! !!! ! .!
!
75
! = ! + ! !!!! ,!
!
!
!
! = ! + !()!
!
!
!
76
! = ! ! !
!
+ 4 !!!!()!
!
! = 1 !!!! + ! .!
!
!
!
Copyright & A K-C
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1.6 -
-
! ! + ! !!! ++ ! +
+ ! , ! = ,!
!
!
!!!
(1.39)
77
! = + !()!
!
! = 1 ! !
!
! = sin +12
( )!()!
!
78
! = 1 ! !
!
! = cos 1 + !()!
!
! = cos + !()!
!
79
! = + 1 + !()!
!
! = + ( )!()!
!
! = cos 1 ! .!
!
Copyright & A K-C
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! , ,!(), , !(, ) = 0,1, , , ()
.
- (1.39),
, ()
0 = !, ! 0 = !! , , !!! 0 = !!!! . (1.40)
(1.39) ! = ( = 0, 1, ,)
! , = ! ( = 0, 1, , ), .. !
. , ! = 1. (1.39)
! + ! !!! ++ ! +
+ ! ! = !
!
!
!!!
, !, , ! . (1.41)
() !() -
! ! ( = 0, 1, , )
()
() ()
(1.41) .
! ! !!!! !!!!! !!!!
( = 0, 1, ,). (1.42)
! ! !
!
!
() ! !!!! !(!!!)
= 0,1, , .
(1.43)
(1.41) :
! + !!!! ++ ! + !!
!!!
= , (1.44)
Copyright & A K-C
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.
(1.44) (1.41)
(1.40). , () -
(1.41), (1.40).
. -
!! + + ! !!! ! = !!!
!
!
!
(1.45)
0 = ! 0 = 0. (1.46)
. () (). (1.46)
!() (),
!! ! .
(1.45)
! +
2 =
1 2
(1.47)
1 !
2=
1 2
. (1.48)
(1.48)
=1
( 1)! ! ! + 1.
, - (1.45),
(1.46),
= ! ! + 1
- :
80 !! + ! !!! ! = !! ,!
!
0 = 0, ! 0 = 1
Copyright & A K-C
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81 ! + ! = !
!
!
!
0 = 1.
82
!! 2! + +
+ 2 cos !! 2 sin ! = cos ,!
!
!
!
! 0 = 0 = 0.
83 !! + 2! + !! 2 sin ! = cos
!
!
!
!
,
! 0 = 0 = 0.
84 !! + + sh + ch ! = ch
!
!
!
!
,
! 0 = 0 = 0.
1.7 (,+)
= + ,!
!
(1.49)
,
.
.!
!
(1.50)
,
( )()!!
!!
= 2 , (1.51)
G(), () .
Copyright & A K-C
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= _ ..
= 0, > 0 , < 0
= ! = , > 00, < 0 (1.52)
(1.51) :
( )()!!
!
= 2_()!() , (1.53)
( ,
).
,
,
= 2 !() . (1.54)
, (1.53) (1.54)
( )()!
!
= 2 _()!() . (1.55)
2_()
:
2_()= !!" = ()!"
!
!
!
!!
.
= (),
2_()= = !".
!
!
,
( )()!
!
= . (1.56)
(1.49).
(1.49),
= +()() (1.57)
Copyright & A K-C
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( )
=()
1 ()
1 , (1.58)
= !".!
!
(1.59)
=12
()1 ()
!"
!!!!
!!!!
(1.60)
(1.49). ,
(1.57) (1.60) , ,
() .
.
= + ! !!! ()!
!
(1.61)
. = , = !!.
=1!
, = !!!!" =1
2 , < 2.
!
!
, :
=1!+
12
,
,
= 2
!( 1). (1.62)
=12
2!( 1)
!"; (0 < < 2)
!!!!
!!!!
. (1.63)
Copyright & A K-C
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(1.63) .
= 0
= 1 , > 1 ,
(1.61)
= ! !!! .!
!
:
!!!
2!( 1)
!" = 2 + 1, res!!!
2!( 1)
!" = ! .
, (1.61)
= 2 + 1 + !
( - ).
:
86 = !! + .!
!
87 = !! + !!! .!
!
88 = cos + !!! .!
!
89 = 1 + ! !!! ; > 0 .!
!
Copyright & A K-C
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1.8 1-
1-
, = , 0 = 0,!
!
(1.64)
() - .
, , , !"(!,!)!"
, !()
0 , 0 . (1.64) x,
, + ,
= ! .
!
!
(1.65)
0 () (1.64)
, , (1.65). ,
0 (1.65)
(1.64).
(, )
0, , (1.65) :
=!()(, )
! , ,
,!
!
(1.66)
. . 2- ,
.
, 0,
(1.65) . .
. (, ) 0, ,
= 0, (1.66) ,
2- . (
3- .) , ,
.
Copyright & A K-C
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.
cos = .!
!
(1.67)
. = , , = cos( )
.
(1.6) ,
cos 0 sin = 1!
!
= 1 + sin .!
!
(1.68)
(1.68) 2- .
, .
,
=1+
1! + 1
,
=! + 1!
=1+
1! 1 +
!
2.
= 1 + !!
! (1.68), ,
(1.67),
.
1-
2- :
90 !!! = sin .!
!
Copyright & A K-C
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91 3!!! = .!
!
92 !!!()!
!
= , 0 = 0.
93 1 ! + ! =!
2.
!
!
94 2 + ! ! = !.!
!
95 sin = !!! 1.
!
!
Copyright & A K-C
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2 2-
2.1
2-
, = !
!
, (2.1)
- , , ,
, , ,
.
, (2.1);
, , ,
,
(, ) !!
!
!
!
.
0, (2.1) ;
0,
, = 0!
!
(2.2)
.
(2.1) (2.2)
, .
(2.1) (2.2)
,
, .
Copyright & A K-C
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. , = sin !"!
!
4 , =
2
!
!
,
, =
2 2
, 0 ;
2 2
, 1.
.
!
4 , =
!
!
= !
4 , +
!
!
, !
!
=
= !
4 2
2 +
2 2
!
!
!
!
=
= !
42 2
!
!
+2
2 !
!
.
sin !"!
,
sin2!
42
sin !"!
2
!
!
+ 2 !
!
sin !"!
2= sin
2
!
42
cos
2+
2!
sin2 !!!
!!!
+
+ 2
cos2
2!
sin2 !!!
!!!
=2
.
Copyright & A K-C
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, !! !
! , , , = sin !"
!
.
,
.
137 = 1, + !" 1 = ! .!
!
138 = sin, + In(1 2cos + !) = 0.!
!
139 = 1 2 sin 1 !
!
, cos ( + ) !
!
= 1.
140 = , , = 3
!
!
+!
6.
, =
(2 )2
, 0 ,
(2 )2
, 1.
141 = ! , + sin = 1.!
!
142 = cos , ! + cos = sin .!
!
143 = !! , 4 ! !!!!
!
= 1 !! .
144 = cos 2, 3 , = 1.!
!
, = sin cos , 0 sin cos , .
Copyright & A K-C
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145 =4C
sin + !! , = , 4
sin sin!
!
!
= 0.
2.2
2-
, = ()!
!
(2.3)
= + , ; ,!
!
(2.4)
, (, ; ), (2.3),
, ; =(, ; )()
(2.5)
, () 0. (, ; ) () :
, ; = , +1 !
!! , ! ,
!
!!!
(2.6)
= 1 +1 !
!!!
!
!!!
, (2.7)
! , =
,
!,
!,
! ,
, ! !, ! !, !
! , !
, ! !, ! !, !
! , !
! !!!
!! . (2.8)
Copyright & A K-C
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! , = , ;
! =
!, ! !, ! !, !
! , !
!, ! !, ! !, !
! , !
!, ! !, ! !, !
! , !
! ! .!
!
!
!
(2.9)
(, ; ) , ()
. , (, )
! , !
!
!
!
, (2.6) (2.7) ,
, .
, ; =(, ; )()
, ,
(). (, ; ).
.
, = !; = 0, = 1.
. ! , = !. ,
! , =! !!!! !!!
! = 0!
!
,
! , =! !! !!!! !!! !!!!! !!! !!!
!
!
!! = 0,!
!
. ,
! , = 0. !:
Copyright & A K-C
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! = !, ! ! = !!!!
!
! = 1!
!
,
! =!!! !!!!!! !!!
!
!
!! = 0!
!
.
, ! = 0.
(2.6) (2.7)
, ; = , = !; = 1 .
,
, ; =(, ; )()
=!
1 .
!!
!
= 1 .
(2.4)
= + !
1 ()
!
!
.
, = !!
= !! +
1 .
.
,
:
146. , = 2 ; 0 1, 0 1.
147. , = ! !; 0 1, 0 1.
148. , = sin cos ; 0 2, 0 2.
149. , = sin sin ; 0 2, 0 2.
Copyright & A K-C
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(2.8) (2.9) ! , !
(2.6) (2.7) ,
:
! , = ! , , !!! , ,!
!
(2.10)
! = !!! , .!
!
(2.11)
, ! = 1 ! , = , (2.11)
(2.10) !,! , ,!,! , ,! ..
. (2.10) (2.11),
, = 2, 0 1, 0 1.
. ! = 1,! , = 2. (2.11),
! = !
!
= !
2 !
!
12
.
(2.10)
! , = 2
2 2 2 = + 2 +
23
.!
!
! = 2 + 2! +23
=13
,!
!
! , = 23
2 2 + 2 +23
= 0,!
!
! = ! = = 0,! , = ! , = = 0.
,
= 1 +2+!
6; , ; = 2 + + 2
23
.
Copyright & A K-C
42
, ; = 2 + + 2 !
!
1 + !!+ !
!
!
.
(2.10) (2.11),
:
150. , = + + 1; 1 1, 1 1.
151. , = 1 + 3; 0 1, 0 1.
152. , = 4 !; 0 1, 0 1.
153. , = !!!; 0 1, 0 1.
154. , = sin( + ) ; 0 2, 0 2.
155. , = sh(); 1 1, 1 1.
:
156. sin + !!
!
= 1.
157. 2 !
!
=6
.
158. sin cos !!
!
= cos 2.
159. !!!!
!
= ! .
160. 4 !!
!
= .
2.3
Copyright & A K-C
43
, = ()!
!
(2.12)
, (2.12)
.
= + ! ! ,!
!!!
(2.13)
!() :
! = , ,!
!
! = , ! = !(, )()!
!
!
!
! 3 = , ! = !(, )()!
!
!
!
..
! , = , ! , ,!
!
! , = , ! , ,!
!
! , = , !!! , ,!
!
(2.14)
= 2, 3,, !(, ) (, ) . !(, ) ,
(2.14), .
Copyright & A K-C
44
! , = ! , !!! , ,!
!
(2.15)
, .
(2.12)
, ; = ! , !!!,!
!!!
(2.16)
, , (, ).
!!
.
:
= 1.!
!
(2.19)
(, ) 1, , ,
! = !(, )!
!
= = 1.!
!
!
!
!
!
Copyright & A K-C
45
, (2.17) , (2.16) < 1.
(2.19), ,
1 = 1,
= ()!
!
.
= 1 , , = 1
(2.19) . , ,
, (2.19)
. > 1 (2.19) . ,
1, = !!!!
,
.
(2.16)
.
: , (, ) .
, :
, , = 0; , , = 0!
!
!
!
(2.20)
x t.
. , = , = !! 1, 1 ,
!! = ! ! = 0,!
!!
!
!!
!! = ! ! = 0.!
!!
!
!!
, .
! , 0,
Copyright & A K-C
46
! , . , ,
(, ).
. , = sin 2 ; 0 2, 0 2.
sin!!
!
2 sin 2 =
=12
cos + 2 3 cos( 2 ) =!!
!
=1213sin + 2 3 + sin( 2 )
!!!
!!!!
= 0
, :
, ; sin 2 ,
(2.16) , ,
.
!(, )
(, )
! , = , ! !, ! !!!, !!!!!
!
!
!
!
!
!
. (2.21)
!(, ) , !(, ) ,
, ,
(, ) .
(, ) ,
!(, ) .
. , = ,
= 0, = 1.
. (2.13), :
! , = ,
Copyright & A K-C
47
! , = = + 2
13
!
!
,
! , = !
!
+ 2
13
= 12
,
! , = 112
= 112! , =
112
+ 2
13
!
!
,
! , = 112
+ 2
13
= 112! , =
12!
!
!
,
! , =112!
=!(, )12!
=112!
+ 2
13
!
!
.
, :
= 2 1:
!!!! , =1 !!!
12!!! ,
= 2:
!! , =(1)!!!
12!!! + 2
13
,
= 1, 2, 3,.
. ! , !(, ) , , =
= !"# (!,!), = 0, = 1.
.
min , = , 0 ,, 1;
, = ! , 0 ,
! , 1.
, ..
, = , .
! , = (, ). :
Copyright & A K-C
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! , = , ! , = , , .!
!
!
!
, = ! , 0
! , 1
, = ! , 0
! , 1
(, ) , !(, )
> .
! , = , , + , , + , , .!
!
!
!
!
!
(0, ) < < ,
(, )(, )!
!
= !! = !! =!!
2 !
!!
!
!
!
=!! 1
2.
, < < ,
, , = !! = !!! !! .!
!
!
!
, 1 > > ,
, , = !! = 1 !!! .!
!
!
!
,
! , = 2 !!! 1 + !!
2 > .
! , < ,
x t ! , > :
! , = 2 !!! 1 + !!
2 < .
,
Copyright & A K-C
49
! , =2 !!!
1 + !!
2, 0
2 !!! 1 + !!
2, 1.
. (, ) , ,
, ,
< .
< :
! , = , , = + + .!
!
!
!
!
!
!
!
. ! , ! , , = 0, = 1
, = + , 0 < , , < 1.
. ! , = (, ),
! , = , , ,!
!
, = + , 0 < , , < 1, , = + , 0 < , < 1.
(, ) , !(, )
: 1) < 2) > .
1) < .
! , = ! + ! + !,
! = + =!
6+!2
,!
!
! = + + =5!
65!
6+32!
32!,
!
!
Copyright & A K-C
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! = + =!
6+!
2 +
2
2+13,
!
!
,
! , = ! 23! ! + 2! +
2
+13
( < , )
2) > .
! , = ! + ! + !,
! = + =32!
5!
6,
!
!
! = =!
6
!
6!2+!
2,
!
!
! = + = 56! +
32! +
2
+13
.!
!
,
! , = 23! ! + ! + 2! +
2
+13
> .
,
! , =23! + ! ! + 2! +
2
+13
, 0 < ,
23! ! + ! + 2! +
2
+13
, < 1.
! ,
( = 3, 4, )
.
161 , = ; = 1, = 1,
162 , = sin ; = 0, = !!
( = 2,3)
163 , = ( )!; = 1, = 1 ( = 2,3)
Copyright & A K-C
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164 , = + sin ; = , =
165 , = !; = 0, = 1.
166 , = ! cos ; = 0, = .
! , :
167. , = !!! ; = 0, = 1.
168. , = ! !!; = 1, = 1.
.
= .!
!
(2.22)
, = ; = 0, = 1. :
! , =
! , = =3
,!
!
! , =13
=3!
,!
!
! , =3!!!
.
(2.16)
, ; = ! , !!! = 3
!!!
=33
,!
!!!
!
!!!
< 3.
(2.18) (2.22)
= + 33
.!
!
Copyright & A K-C
52
, =
=3
3 ,
3.
:
169 , = !!!; = 0, = 1.
170 , = sin cos ; = 0, = !!
.
171 , = !; = 1, = 1.
172 , = 1 + 1 ; = 1, = 0.
173 , = !!; = 1, = 1.
174 , = ; = 1, = 1.
2.4
(, ) 2-
,
, . .
, = ! ! .!
!!!
(2.23)
!() ! ( = 1,2, . . . ,)
, .
(2.23)
! ! !
!!!
= ()!
!
(2.24)
.
(2.24)
Copyright & A K-C
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= + !()!
!!!
!()()!
!
(2.25)
! = ! , = 1, 2, . . . , .!
!
(2.26)
(2.25)
= + !!
!
!!!
, (2.27)
! ( ).
,
! = 1, 2, . . . , .
(2.27) (2.24),
! ! + !! !
!!!
!
!
! = 0.!
!!!
! = 1,2, . . . ,
,
! ! + !! !
!!!
= 0!
!
! ! ! ! = ! = 1,2, . . . , .!
!
!
!
!
!!!
!" = ! ! , !
!
!
= ! ,!
!
,
! !" ! = ! ( = 1,2, . . . ,)!
!!!
Copyright & A K-C
54
:
1 !! ! !" ! !! ! = !!"! + 1 !! ! !! ! = !
!!! !!! + (1 !!) ! = !
(2.28)
!
.
=
1 !! !" !!!" 1 !! !!
!! !! 1 !!
. (2.29)
0 , (2.28)
!,!, . . . ,!,
! =1
()
1 !! !!!!! !!!! !!!" !!!!! !!!! !!
!! !"!!! !"!! 1 !!
(2.30)
= 1,2, . . . , .
(2.24) () ,
= + !!
!
!!!
,
! = 1,2, . . . , (2.30).
. (2.28) ,
(2.27) ! , ! , . . . , !()
(2.27) ()
(2.26), .
.
Copyright & A K-C
55
cos + ! sin + cos sin = .!
!!
(2.31)
. :
= () cos + sin !()!
!!
+ cos () sin + .!
!!
!
!!
:
! = () cos ; ! = ! ;!
!!
!
!!
! = () sin ,!
!!
(2.32)
!,!,! . (2.31)
= ! + ! sin + ! cos + . (2.33)
(2.33) (2.32),
! = (! + ! sin + ! cos + )!
!!
cos ,
! = ! + ! sin + ! cos + !,!
!!
! = (! + ! sin + ! cos + )!
!!
sin
! 1 cos !
!!
! sin cos ! cos! = cos !
!!
!
!!
!
!!
,
! !!
!!
+ ! 1 ! sin !
!!
! ! cos = !,!
!!
!
!!
! sin !
!!
! sin! + ! 1 cos sin !
!!
!
!!
= sin .!
!!
Copyright & A K-C
56
,
!,!,!: ! ! = 0,
! + 4! = 0,
2! ! + ! = 2
(2.34)
=
1 0
0 1 4
2 1
= 1 + 2!! 0.
(2.34)
! =2!
1 + 2!!; ! =
8!
1 + 2!!; ! =
21 + 2!!
.
!,!,! (2.33),
:
=2
1 + 2!! 4 sin + cos + .
:
180 4 sin! = 2 .
!!
!
181 e!"#$%& ! = tg .!
!
182 tg = ctg .
!!
!
183 cos( ln )() = 1.!
!
Copyright & A K-C
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184 arccos () =1
1 !.
!
!
185 ln1
!
= 1 ( > 1).!
!
186 ( ln ln ) =65(1 4).
!
!
187 sin cos = sin .
!!
!
188 sin = .!!
!
189 sin( ) = cos .!
!
190 (sin cos sin 2 cos 2 + sin 3 cos 3) = cos .!!
!
191 12
12
3! 1 +12(3! 1) = 1.
!
!!
2.5
2-
, = 0!
!
(2.35)
0 ,
() .
Copyright & A K-C
58
,
x 0 ,
(2.35) , ,
,
.
= 0 , = 0
(2.35) , 0.
, = ,
, ,
;
.
.
! !()!
!!!
= 0!
!
(2.36)
=
1 !! !" !!!" 1 !! !!
!! !! 1 !!
= 0 (2.37)
. ( ) -
1 !! ! !"! !!!= 0,
!"! + 1 !! ! !!!= 0 .
!! ! !!! + 1 !! != 0
, (2.38)
!" ! , = 1,2, , ,
.
Copyright & A K-C
59
(2.37) (1 ),
(2.36) ;
! = 1,2, ,
!! , !
! , , !! !,
!! , !
! , , !! !
...............
!(!), !
(!), , !(!) !,
(2.38).
(2.36), .. ,
! = !!
!
!!!
! ,
! = !!
!
!!!
! ,
! = !!
!
!!!
! .
, ,
.
()
, ..
, , . , , ,
, = 0,!
!
, !(!) , ( () =
= !!!!, . 177).
.
, .. () ,
Copyright & A K-C
60
, ,
, ,
.
.
cos! cos 2 + cos 3cos! = 0!
!
.
.
= cos! cos2 + cos3 !
!
!
!
cos! = 0
!= cos2 !
!
!= cos!!
!
(2.39)
= ! cos! + ! cos3. (2.40)
(2.40) (2.39),
! 1 os!!
!
cos2 ! cos3 cos2 = 0,!
!
! cos!!
!
+ ! 1 cos! cos3 !
!
= 0.
(2.41)
cos!!
!
cos2 =4
, cos3 cos2 = 0!
!
,
cos!!
!
= 0, cos!!
!
cos3 =8
, (2.41)
Copyright & A K-C
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1 4
!= 0
1 8
!= 0 (2.42)
1 4
0
0 1 8
= 0.
! =4
, ! =8
.
= !! (2.39)
0 != 0,12
!= 0,
!= 0, a ! . ! = !cos!
, ! = 1, ! = cos!.
! =!! (2.38)
(1) != 0,
0 != 0,
!= 0, ! , ! = !cos3,
, ! = 1, ! = cos3.
, :
! =4
, ! =8
;
:
! = cos!, ! = cos3.
.
1.
Copyright & A K-C
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3 2 !
!
= 0.
. ,
= (3 2) .!
!
= !
!
, (2.43)
= 3 2 . (2.44)
(2.44) (2.43)
1 3! 2 !
!
= 0. (2.45)
3! 2 !
!
= 0,
(2.45) = 0, , , 0.
,
= 0, ,
.
2.
= 0!
!
.
= ! !, (2.46)
Copyright & A K-C
63
!= ,!
!
!= .!
!
(2.47)
(2.46) (2.47),
1 25 ! +
3!= 0
2! + 1 +
25 != 0
(2.48)
=1
25
3
2
1 +25= 1 +
!
150.
, (2.48)
!= 0 != 0, ,
, : 0. , (2.46)
.
:
198 sin! = 0
!!
!
.
199 sin = 0!!
!
.
200 sin sin = 0!!
!
.
Copyright & A K-C
64
201 cos + = 0!
!
.
202 45!In 9!In = 0!
!
.
203 2 4! = 0.!
!
204 5! + 4! = 0!
!!
.
205 5! + 4! + 3 = 0!
!!
.
206 ch sh = 0!
!!
.
207 ch !sh = 0!
!!
.
208 ch ch = 0!
!!
.
2.6 ,
= ,!
!!
(2.49)
( ) ,
OX,
Copyright & A K-C
65
= . (2.50)
, (2.49)
!! = cos ,
!! = sin ,
= 1, 2, , (2.51)
! =1!
= 1, 2, , (2.52)
! ():
! =1
cos!
!!
, = 1, 2, . (2.53)
, !
cos , sin , !
. ! 1
(2.49),
! =1!
, ! =1
,!
!!
, , cos
=1!
,!
!!
(2.54)
! =1
cos .!
!!
= ,
cos!
!!
= cos =!!!
!!!
= cos cos!!!
!!!
+ sin sin !!!
!!!
= ! cos,
Copyright & A K-C
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,
!
().
,
cos = 1!
cos ,!
!!
, cos (2.54).
, sin
(2.54),
!!! !
.
225
= cos!!
!!
.
226 ,
, =12
1 !
1 2 cos + ! ( , )
< 1 1, sin, cos,
1, 1 ! , 1 !.
227
= !
!!
,
= ! ( ) 2.
Copyright & A K-C
67
2.7
! ! !
!!!
= 0,!
!
(2.55)
(.. ()0),
: () 0.
(.. ()=0),
(2.55) , ,
.
(2.55)
.
, !, !, , !
(2.55), p ,
, ,
! ( = 1, 2, , ).
.
cos! cos 2 + cos! cos 3 = 0.!
!
.
= !!
, ! =!!
,
! = cos!, ! = cos 3.
= cos!; =4
;
= cos 3; =8
;
= 0; 4
, 8
,
Copyright & A K-C
68
.
= 0.
231 cos + = 0.!
!
232 arccos = 0.!
!
233 2()
1 + cos 2 = 0.
!!
!
234 14
= 0.!
!!
235 + 6 ! 2 = 0.!
!
2.8
2-
, = ()!
!
(2.56)
, (, ) :
(, ) (, ) .
()
! ( = 1, 2, )
Copyright & A K-C
69
, !
!
= 0, (2.57)
(2.56)
= !
!
!
!!!
! . (2.58)
! (2.56),
! = ! ,!
!
(2.59)
, (2.58),
, .
,
= !, ( !, ), (2.56),
, . ,
,! = 0
!
!
! = 0, = 1, 2, , ,
(2.60)
.. ,
!, .
(2.45) ,
= !
!
!
!!!!!
! + !! ++ !! , (2.61)
!, !,, ! .
Copyright & A K-C
70
, = !
!
!!!
! (2.62)
(2.58) (2.61)
.
(2.56), .. ,
! (2.57),
(2.56) : = .
.
, !
!
= , (2.63)
, = 1 , 0 ,
1 , 1.
.
! = !!; ! = sin, = 1, 2,
!, (2.63)
= !
+ !!
!
!!!
sin. (2.64)
! :
! = sin !
!
= =
= sin
=
= 1
cos =
= cos
!
!+
1
cos !
!
= cos
sin! !
!
=1 !!!
.
(2.64),
=
(1)!!!
( + !!)
!
!!!
sin.
= !! (2.63) ,
Copyright & A K-C
71
! =1 !!!
0.
.
, = cos,!
!
, = + 1 , 0 ,
+ 1 , 1.
. :
! = 1, ! = !! = 1, 2,
:
! = !, ! = sin + cos, ( = 1, 2,).
1 !!,
= !!
1+
! + !!
(sin + cos)!
!!!
,
! = !!
!
cos = 1 + 1 + !
,
! = cos!
!
sin + cos = 0, 12
, = 1,
= cos + 1 + 1 + !
!
1
2( + !)
(sin + cos) .
=1 = ! ( = 1) ,
, .. cos ,
! = ! , ! = sin + cos.
Copyright & A K-C
72
= !! , = 2,3, . .,
, (2.61):
= cos + 1 + 1 + !
!
1
2( + !)
(sin + cos) +
+ (sin + cos),
.
.
, ,
.
.
.
, !
!
= ! , (2.65)
, =
sh sh( 1)sh1
, 0 ,
sh sh ( 1)sh 1
, 1.
.
= ! +sh( 1)
sh 1sh +
sh sh 1
!
!
sh 1 .!
!
(2.66)
,
! = ! +ch 1
sh 1sh +
sh 1sh 1
!
!
sh +
+ ch sh 1
sh 1 !
!
sh sh 1
sh 1 ,
Copyright & A K-C
73
!! = ! +sh 1
sh 1sh +
shsh 1
!
!
sh 1 !
!
+
+ ch 1
sh 1sh
ch sh 1
sh 1
!! = ! + + .
(2.66) = 0 = 1 , , 0 = 1 , 1 = .
!! ( + 1) = ! , (2.67)
0 = 1, 1 = . (2.68)
:
1) + 1 = 0, .. = 1. (2.67) !! = ! .
= ! + ! + ! .
(2.68),
! ! ! + 1 = 1,
! + ! + = ,
!= 0, != 0, , , = ! .
2) + 1 > 0, .. > 1, 0. (2.67)
= !ch 1 + + !sh 1 + !!
!.
(2.68) ! !
! 1= 1
!ch 1 + + !sh 1 + = ,
!= 1 +1
, != ch 1 + sh 1 +
1 +1
.
Copyright & A K-C
74
= 1 +1
sh 1 + (1 )
sh 1 + !
.
3) + 1 < 0, . . < 1. + 1 = ! .
(2.67)
= ! cos + ! sin !
1 + !.
(2.68)
! +1
1 + != 1,
! cos + ! sin = !
1 + !.
(2.69)
:
) sin =0.
!=!
1 + !, !=
( cos)!
1 + ! sin ,
,
=!
1 + !cos +
cos sin
sin +e!
1 + !,
= 1.
) sin = 0, .. = , = 1,2, .
(2.69) , , (2.65)
.
+ 1 + !! , !
!
= 0 (2.70)
, ..
! = 1 + !!
Copyright & A K-C
75
,
! = sin
(2.70).
:
236 !
4 , =
2
,!
!
, =
(2 )2
, 0 ,
(2 )2
, 1.
237 + , = ! ,!
!
, =
sh sh( 1)sh 1
, 0 ,
sh sh( 1)sh 1
, 1.
238 , = ! !,!
!
, = , 0 ,
, 1.
239 2 , = cos 2 ,
!!
!
, =sin cos , 0 ,
sin cos , 1.
240 , = 1,!
!
, =sin cos , 0 ,
sin cos , .
241 , = ,!
!
, = + 1 ( 3), 0 ,
+ 1 ( 3), 1.
242 , = ( )!,!
!
, =sin +
4
sin 4
, 0 ,
sin +4
sin 4
, .
Copyright & A K-C
76
243 , = + 1,!
!
, =!!sh , 0 ,
!!sh , 1.
244 , !
!
= 2 1, , =
ch ch( + 1)sh 1
, 0 ,
ch ch( + 1)sh 1
, 1.
Copyright & A K-C
77
1. 2- :
= + , .!
!
(1)
. (1)
= + , ; .!
!
(2)
(, ; ) - (1)
, ; = !!!! , ,!
!!!
(3)
!!!(, )
!!! , = , ! , ,!
!
! , = , , = 1, 2, .
(4)
. (1)
!() , = 0, 1, 2,,
! = + , !!! .!
!
(5)
!() ().
2-
Copyright & A K-C
78
= + .!
!
(6)
.
, () ,
, ,() (. )
(6)
,
=()
1 (),() 1. (7)
() (6).
1-
, ()!
!
= , (8)
(, ) 0,
2-
=!()(, )
!! , ,
.!
!
(9)
1-
= ()!
!
(10)
. , ()
-
, , () ()
, (10)
,
Copyright & A K-C
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=()()
. (11)
() (10).
2. . 2- :
, = .!
!
(12)
. (12)
= + , ; ,!
!
(13)
, ; =(, ; )()
,() 0, (14)
(12).
, ; = , +1 !
!! , ! ,
!
!!!
(15)
= 1 +(1)!
!
!
!!!
!! . (16)
! , , !
! , = !
!
, , ! (, !)
!, !, ! (!, !)
!, !, ! (!, !)
.
! , ! , ! (! , !)
!! ,!
!
(17)
! , = , .
Copyright & A K-C
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! = !
!
!, ! !, ! (!, !)
!, ! !, ! (!, !)
!, ! !, ! (!, !)
.
! , ! ! , ! (! , !)
!! .!
!
(18)
:
! , = ! , , !!! , ,!
!
(19)
! = !!! , , ( = 1, 2, )!
!
(20)
! = 1,! , = , .
. (12)
.
= + ! ! ,!
!!!
(21)
!() :
!() = , ,!
!
! = , ! = ! , ,!
!
!
!
! = , ! = ! , ()!
!
!
!
..
! , = , , ,!
!
Copyright & A K-C
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! , = , !(, )!
!
! , = , !!!(, )!
!
, = 2, 3, . (22)
! , = (, ).
! , , (12),
.
:
! ! !
!!!
= .!
!
(23)
(23)
= + !! ,!
!!!
(24)
!
1 !! ! !"! !!! = !,
!"! + 1 !! ! !!! = !,
!!! !!! + 1 !! ! = ! .
(25)
!" = ! ! ; ! = ! !
!
!
!
(26)
, = 1, 2, , .
(25) , (23)
(24).
.
0,
2-
Copyright & A K-C
82
, = 0!
!
(27)
() 0,
(21) , ,
,
.
,
= , ,
.
! ! !
!!!
!
!
= 0. (28)
=
1 !! !" !!!" 1 !! !!
!! !! 1 !!
= 0, (29)
() - (25); .
(29) p (1 ) ,
(27) p !, !, , !,
! = !! ! ( = 1, 2, , )
!
!!!
(30)
!(!) ( = 1, 2, ,) - (25),
! ( = 1, 2, , ) .
()
(), .. (, ; ).
Copyright & A K-C
83
, (, )
,
.
2- :
, = ,!
!
(31)
, = , .
! ( = 1, 2, ) - , ! ( = 1, 2, ) -
, .
a) ! ( = 1, 2, ),
(31) ,
= !
!! ,
!
!!!
(32)
! = ! .!
!
(33)
(32) , .
b) ,
= ! , q ( ! ),
(31) ,
()
!, .. q
! = 0 = 1, 2, , .!
!
(34)
Copyright & A K-C
84
= !
!! + !! + !! ++ !! ,
!
!!!!!
(35)
!, ,! - , ! , ,!() -
, ! .
q (34) , ! ,
(, ) (31) :
= .
2- ,
:
a) , ()!
!
= 0, (33)
, =
( )
, ,
( )
, .
:
! =
!
:
! = sin
= 1, 2, .
) , ()!
!!
+12
= 0,!
!!
, =
12ln1 + 1
, ,
12ln1 + 1
, .
Copyright & A K-C
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: ! = + 1 . :
! = !(), !() ,
! =1
2!!!
!(! 1)! .
! = 1 !(), ,
+ 1 !!! = 2 + 1 ! + !!! ,
= 2, 3,.
) , = 0,!
!
, =
12
!, ,
12
!, .
: ! = !! , ! -
! = 0. : ! = ! ! , , !()
1- . 1-
! =2
! 1 !
! + + 12
!!.
!
!!!
) , !!
!
= 0,
, =
!!!!
!!
, ,
!!
!
!!!!
!!
, .
!!
!
:
Copyright & A K-C
86
! = + 1.
:
! = !!! ! ,
!() - ,
! = !!
!!!! .
!!! = 2 + 1 ! !!!! 1 ,
! = 1
! = + 1.
) , = 0,!!
!!
, =
1!!!!!
! !!! !!!, ,!!
!
!!
!!
1!!!!!
! !!! !!!, .!!
!
!
!!
: ! = 2 + 1 ( = 0, 1, 2, ).
:
!(0 = !!
!
! ! ,
!() - , :
! = 1 !!! !
!!!! =
= 2 ! 1
1!(2)!!! +
1 2 ( 3)2!
(2)!!! +
! = 1 ! = 2,
, :
!!! = 2! 2!!! .
Copyright & A K-C
87
() ()
() 1
!" 1
! !!
!!" !
!!!
sin
! + !
cos
! + !
sh
! !
ch
! !
!" sin
! + !
!" cos
! + !
!"sh
! !
!"ch
! !
sin 2
! + ! !
cos ! !
! + ! !
sh 2
! ! !
Copyright & A K-C
88
ch ! + !
! ! !
1sin
!
!(! + !)
2
!! !
( > 0) 1
!"() ( )
( > 0, ) !!"()
!() (0)
! () ! !!!!! ! (0)!!!
!!!
()
1()
1 !!() !()!
()
()!
!
! !()
! !( )!
!
! !()
Copyright & A K-C
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1
1.
= cos + .!
!
2.
! = 2 3 ! !!! ! + ! ,!
!
!
!
! = 3 ! + 2 ! .!
!
!
!
3. -
!! + + sh + ch ! = ch !
!
!
!
,
! 0 = 1, 0 = 1.
4.
= !!! + .!
!
5. 1-
! !!! = sin 2.!
!
6. , = cos
3 , = 1!
!
, , = sin cos, 0 ,sin + cos, .
7. , = !cos,
= 0, = .
Copyright & A K-C
90
2
1.
= ! + 2 cos .!
!
2.
! = sin + ! ,!
!
! = 1 cos ! .!
!
3. -
!! + + sh + ch ! = ch !
!
!
!
,
! 0 = 1, 0 = 1.
4.
= 3 + ! !!! .!
!
5. 1-
cos = 2!.!
!
6. , = !!
4 ! !!! = 1 !!!
!
.
7. , = ! , = 0 ,
= 1.
Copyright & A K-C
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3
1.
= 1 + 2 cos .!
!
2.
! = !! + ! ,!
!
! = 1 ! !!! ! .!
!
3. -
!! + 2! + !! sin ! = cos !
!
!
!
,
! 0 = 0 = 0.
4.
= cos 3 + ! !!! .!
!
5. 1-
sin = 2.!
!
6. , = cos
! + cos =!
!
sin .
7. , = + sin ,
= , = .
Copyright & A K-C
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4
1.
= sh ch .!
!
2.
! = ! + ! !
!
!!!! ,!
!
! = ! !
!
+ ! .!
!
3. -
!! 2! + + 2 cos !! + sin ! = cos !
!
!
!
,
! 0 = 0 = 0.
4.
= !!! + .!
!
5. 1-
3 + ! ! !
!
= 3.
6. , = !
sin !
!
= 1.
7. , = !,
= 1, = 1.
Copyright & A K-C
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5
1.
= 1 2 4! + 3 6 4 ! .!
!
2.
! = ! + ! !
!
+ 4 !!!! ,!
!
! = 1 !!!! !
!
+ ! .!
!
3. -
! + ! = !
!
!
!
,
0 = 1.
4.
= 2 + ! !!! .!
!
5. 1-
1 ! + ! !
!
= !.
6. , =
, !
!
= 3+!
6, , =
(2 )2
, 0 ,
(2 )2
, 1.
7.
sin !
!
= cos .
Copyright & A K-C
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6
1.
= sh .!
!
2.
! = + ! ,!
!
! = 1 ! ,!
!
! = sin +12
! !
!
.
3. -
! + ! !! ! !
!
= !! ,
0 = 0, ! 0 = 1.
4. a
= cos 2 + ! !!! .!
!
5. 1-
! !!! !
!
= 3.
6.
, = 2 , = 0, = 1.
7.
sin !!
!
= .
Copyright & A K-C
95
7
1.
= sin + .!
!
2.
! = 1 ! ,!
!
! = cos 1 + ! ,!
!
! = cos + ! !
!
.
3. -
! + + ! !! ! !
!
!
!
= !! ,
0 = ! 0 = 0.
8. a
= !!! + ! !!! .!
!
9. 1-
3! !!! !
!
= 2.
10.
, = sin cos , = 0, = 2.
11.
sin cos
!!
!
= sin .
Copyright & A K-C
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8
1.
= + sin .!
!
2.
! = + 1 + ! ,!
!
! = + ! ,!
!
! = cos 1 ! !
!
.
3. -
! + + sh !
!
+ ch !
!
= ch ,
0 = ! 0 = 0.
4. a
= !!! + .!
!
5. 1-
! !!! !
!
= sin 2.
6.
, = + + 1, = 1, = 1.
7.
ln ln !
!
=65
1 4 .
Copyright & A K-C
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9
1.
= ! + .!
!
2.
! = ! + ! ,!
!
!
!
! = 1 + !!!! !
!
+ ! .!
!
3. -
+ ! !!! !
!
= !! ,
0 = 0, ! 0 = 1.
4. a
= + ! !!! .!
!
5. 1-
!!! !
!
= cos .
6.
, = !!!, = 0, = 1.
7.
cos ! sin + cos sin !
!!
= .
Copyright & A K-C
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10
1.
= + .!
!
2.
! = + ! !!!! ,!
!
!
!
! = 1 + ! !
!
+ ! .!
!
3. -
! + ! !
!
!
!
= ,
0 = 1.
4. a
= !! + .!
!
5. 1-
sin !
!
= cos .
6.
, = 1 + 3, = 0, = 1.
7.
tg
!!
!!!
= ctg .
Copyright & A K-C
99
11
1.
= 3 + ! + .!
!
2.
! = 3 ! + ! ,!
!
!
!
! = 1 4 ! !
!
+ 3 ! .!
!
3. -
!! 2! + + 2 cos !! !
!
+ 2 sin !
!
= cos ,
0 = 0 = 0.
4. a
= !! + !!! .!
!
5. 1-
ch !
!
= sh .
6. C a
sin !!
!
= 1.
7.
sin cos !!
!
= 0.
Copyright & A K-C
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12
1.
= 1 + ! + .!
!
2.
! = !! ! + 2 !!!! ,!
!
!
!
! = + ! !!! ! !
!
+ ! .!
!
3. -
!! + 2! + !! !
!
2 sin ! !
!
= cos ,
0 = ! 0 = 0.
4. a
= cos + !!! .!
!
5. 1-
sin !
!
= 1 + !.
6. C a
2 !
!
=6
.
7.
sin sin !!
!
= 0.
Copyright & A K-C
101
13
1.
= 6 + ! + .!
!
2.
! = 2 ! 4 ! ,!
!
!
!
! = 2 ! !
!
! .!
!
3. -
!! + sh !
!
+ ch ! !
!
= ch ,
0 = ! 0 = 0.
4. a
= 1 + ! !!! .!
!
5. 1-
ch !
!
= .
6. C a
sin cos !!
!
= cos 2.
7.
cos + !
!
= 0.
Copyright & A K-C
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14
1.
= 5 + + .!
!
2.
! = 1 + ! + ! ,!
!
!
!
! = 1 + ! !
!
! .!
!
3. -
!! + + sh !
!
+ ch ! !
!
= ch ,
0 = 1, ! 0 = 1.
4.
= 7 + ! !!! .!
!
5. 1-
sh !
!
= ch .
6. C a
!!! !
!
= ! .
7.
45! ln 9! ln !
!
= 0.
Copyright & A K-C
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15
1.
= 1 + 2 + sin .!
!
2.
! = + ! + ! ,!
!
!
!
! = 2 + ! !
!
+ 2 ! .!
!
3. -
!! + ! !!! !
!
= !! ,
0 = 0, ! 0 = 1.
4.
= 2 + ! !!! .!
!
5. 1-
! !!! !
!
= ! .
6. C a
4 ! !
!
= .
7.
5! + 4! !
!!
= 0.
Copyright & A K-C
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1. , .. / .. , ..
, .. . .: , 1968. 192 .
2. , . . /. . , . .
. - -. . .: , 2009. 160 c.
3. , . . /
. . . -. . .: , 2005. 176 c.
Copyright & A K-C
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