TRIGONOMETRY JEE Mains Super40 Revision Series€¦ · Watch Free Video Solution on Doubtnut 5 17468 JEE Mains Super40 Revision Series TRIGONOMETRY , , find Watch Free Video Solution

JEE Mains Super40 Revision Series

TRIGONOMETRY

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1 8646

JEE Mains Super40 Revision Series TRIGONOMETRY

The number of integral values of for which the equation has a solution is (1) (2) (3) (4)

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2 9793


The value of is (a) (b) (c) (d)


3 11683


If , then the number of real values of x, which satisfy the equation is : (1) 3 (2) 5 (3) 7 (4) 9


4 11799 JEE Mains Super40 Revision Series TRIGONOMETRY

If then

k 7 cosx + 5 sinx = 2k + 14 8 10 12

cot(2

∑n= 1

cot − 1(1 +n

∑k= 1

2k))23

25

25

23

23

24

25

26

0 ≤ x < 2πcosx + cos 2x + cos 3x + cos 4x = 0,

sin− 1( ) + sin− 1( ) = 2 tan− 1 x2a

1 + a22b

1 + b2x =

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5 17468


, , find


6 19684


If then the value of is: (2) (3)

(4)


7 22037


The equation


8 22312


Let be a positive integer such that Then (b)

c) d)



The value of

√2 cosA = cosB + cos3 B √2 sinA = sinB − sin3 B sin(A − B)

5(tan2 x − cos2 x) = 2 cos 2x + 9, cos 4x2

9−

7

9

−3

5

1

3

2 sin2 x = x2 + x− 2; 0cos2 x

2

n + = .sinπ

2n

cosπ

2n

√n

26 ≤ n ≤ 8

4 < n ≤ 8 4 ≤ n ≤ 8 4 < n < 8

(1 + )(1 + )(1 + )(1 + )iscosπ

8

cos(3π)

8

cos(5π)

8

cos(7π)

8

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(a)1/4 (b) 3/4 (c) 1/8 (d) 3/8


10 22432


If , then (a) (b)

(c) (d) none of these


11 22457


If then (a)

(b)

(c)

(d)none of

these


12 22512


The number of solutions of the pair of equations in the interval is



Given then for all real (a) (b) (c)

y = , x ∈ (0, )sin4 x − cos4 x + sin2 x cos2 x

sin4 x + cos4 x + sin2 x cos2 x

π

2− ≤ y ≤

3

2

1

2

1 ≤ y ≤1

2− ≤ y ≤ 1

5

3

α + β + γ = 2π,

tan( ) + tan( ) + tan( ) = tan( )tan( )tan( )α

2

β

2

γ

2

α

2

β

2

γ

2

tan( )tan( ) + tan( )tan( ) + tan( )tan( ) = 1α

2

β

2

β

2

γ

2

γ

2

α

2

tan( ) + tan( ) + tan( ) = − tan( )tan( )tan( )α

2

β

2

γ

2

α

2

β

2

γ

2

2 sin2 θ − cos(2θ) = 0, 2 cos2 θ − 3 sin θ = 0 [0, 2π]

A = sin2 θ + cos4 θ, θ, 1 ≤ A ≤ 2 ≤ A ≤ 13

4

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(d)


14 22518


where . Number of pairs of

which satisfy both the equations is 0 (b) 1 (c) 2 (d) 4


15 22556


The general values of satisfying the equation is

(b) (d)


16 22558


The number of solutions of the equation lying in the interval is 0 (b) 1 (c) 2 (d) 3


17 22611


The set of all x in satisfying is given by



≤ A ≤ 113

16≤ A ≤

3

4

13

16

cos(α − β) = 1and cos(α + β) = ,l

eα, βμ ∈ [ − π, π]

α, β

θ 2 sin2 θ − 3 sin θ − 2 = 0 (n ∈ Z).

nπ + ( − 1)n π

6nπ + ( − 1)

n π

2nπ + ( − 1)

n 5π

6nπ + ( − 1)

n 7π

6

tanx + secx = 2 cosx[0, 2π]

( , )−π

2

π

2|4 sinx − 1| < √5

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Let Then is (a) only when (b) forall real (c) for all real (d) only when


19 22690


Consider the system of linear equations in Which of the

following can be the value of for which the system has a nontrivial solution

none of these


20 22696


The equation in the variable has real roots.

The can take any value in the interval (a) (b) (c) (d)


21 22753


If no solution of lies on the line then a



Let Then the set of all satisfying is

f(θ) = sin θ(sin θ + sin 3θ). f(θ) ≥ 0 θ ≥ 0 ≤ 0θ ≥ 0 θ ≤ 0 θ ≤ 0

x, yandz :(sin 3θ)x − y + z = 0(cos 2θ)x + 4y + 3z = 0 3x + 7y + 7z = 0

θ

nπ + ( − 1)n , ∀n ∈ Zπ

6nπ + ( − 1)n , ∀n ∈ Z

π

3nπ + ( − 1)n , ∀n ∈ Z

π

9

(cos p − 1)x2 + (cos p)x + sin p = 0 x

p (0, 2π) ( − π, 0) ( − , )π

2

π

2(0, π)

3 sin y + 12 sin3 x = a y = 3x,a ∈ ( − ∞, − 9) ∪ (9, ∞) a ∈ [ − 9, 9] aa ∈ { − 9, 9} noneofthese

f(x) = x2andg(x) = sinxf or allx ∈ R. x(fogogof)(x) = (gogof)(x), where(fog)(x) = f(g(x)),±√nπ, n ∈ {0, 1, 2, .} ±√nπ, n ∈ {1, 2, .}

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23 22776


For the equation sin has (A)infinitely manysolutions (B)three solutions (C)one solution (D)no solution


24 22933


If then which of the following is not true? (a)

(b) (c) (d) none of these


25 22959


equals a) b) c) d)


26 23013


The value of is (b) (c) (d) none of

these


+ 2nπ, n ∈ {, − 2, − 1, 0, 1, 2}π

22nπ, n ∈ {, − 2, − 1, 0, 1, 2, }

x ∈ (0, π), sinx + 2 x − sin 3x = 3

= k(k ≠ 1)tan 3A

tanA=

cosA

cos 3A

k − 1

2

=sin 3A

sinA

2k

k − 1=

cot 3A

cotA

1

k

(sec 2x − tan 2x) tan(x − )π

4tan( − x)

π

4cot(x − )

π

4tan2(x + )

π

4

tan[cos − 1( ) + tan− 1( )]4

5

2

3

6

17

7

16

16

7

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The equation has one negative solution one positive solution no

solution more than one solution


28 23105


Which of the following is the solution set of the equation

(a)(0.1) (b) (c) (d)


29 23124


The value of (b) (c) (d)

independent of


30 27849


The domain of definition of the function for realvalued is

(b) (c) (d)



If then is equal to (a)

3− 1x − πx − = 0π

2

2 cos − 1 x = cot − 1( )?2x − 1

2x√1 − x2( − 1, 1) − {0} ( − 1, 0)

( − 1, 1)

tan− 1( ) − cot − 1( )isx cos θ

1 − x sin θ

cos θ

x − sin θ2θ θ

θ

2θ

f(x) = √sin− 1(2x) +π

6x

[ − , ]1

4

1

2[ − , ]

1

2

1

2( − , )

1

2

1

9[ − , ]

1

4

1

4

u = cot − 1 √tanα − tan− 1 √tanα, tan( − )π

4

u

2√tanα

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(b) (c) (d)


32 44201


The number of real solutions of is a.

b. one c. two d. infinite


33 44373


The number of distinct real roots of in the interval

is (a) (b) (c) (d)


34 45899


If then is equal to


35 50042


If then the differencebetween the maximum and minimum values of is given by : (a) (b)

(c) (d)


√cosα tanα cotα

tan− 1 √x(x + 1) + sin− 1 √x2 + x + 1 =π

2zero

∣∣ ∣∣

sinx cosx cosx

cosx sinx cosx

cosx cosx sinx

∣∣ ∣∣

= 0

− ≤ x ≤π

4

π

40 2 1 3

0 < x < 1, √1 + x2[{x cos(cot − 1 x) + sin(cot − 1 x)}2 − 1]12

u = √a2 cos2 θ + b2 sin2 θ + √a2 sin2 θ + b2 cos2 θ2,u2 (a − b)2

2√a2 + b2 (a + b)2 2(a2 + b2)

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36 61318


The general solution ofthe trigonometrical equation for is given by (a) (b) (c)

(d) non of these


37 87428


If we consider only the principal values then the value inverse trigonometric functions

then the value of is (a) (b) (c) (d)


38 1241998


If the sum of all the solutions of the equation

in is then k is equal to


39 1269712


If then the value of can be (a) (b)

(c) (d)


sinx + cosx = 1

n = 0, ± 1, ± 1 x = 2nπ x = 2nπ +π

2x = nπ + ( − 1)

n−

π

4

π

4

(cos − 1( ( − sin− 1) )1

5√2

4

√17

√29

3

29

3

√3

293

29

8 cosx. (cos( + x)cos( − x) − ) = 1π

6

π

6

1

2[0, π] kπ

θ = tan− 1(2 tan2 θ) − tan− 1( tan θ)1

3tan θ −2

12

32

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40 1408461


The value of for which is (a) (b) (c) (d)


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x sin(cot − 1(1 + x)) = cos(tan− 1 x)1

21 0

−1

2
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TRIGONOMETRY JEE Mains Super40 Revision Series€¦ · Watch Free Video Solution on Doubtnut 5 17468 JEE Mains Super40 Revision Series TRIGONOMETRY , , find Watch Free Video Solution