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Class:X Mathematics
Website: www.std10th.blogspot.in
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Page 193 »Exercise 8.4 »
Question 1:
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.
Answer :
We know that,
will always be positive as we are adding two positive quantities.
Therefore,
We know that,
However,
Therefore,
Also,
Question 2:
Write all the other trigonometric ratios of ∠A in terms of sec A.
Answer :
We know that,
Class:X Mathematics
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Also, sin2 A + cos
2 A = 1
sin2 A = 1 − cos
2 A
tan2A + 1 = sec
2A
tan2A = sec
2A − 1
Question 3:
Evaluate
(i)
(ii) sin25° cos65° + cos25° sin65°
Answer :
(i)
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(As sin2A + cos
2A = 1)
= 1
(ii) sin25° cos65° + cos25° sin65°
= sin225° + cos
225°
= 1 (As sin2A + cos
2A = 1)
Question 4:
Choose the correct option. Justify your choice.
(i) 9 sec2 A − 9 tan
2 A =
(A) 1
(B) 9
(C) 8
(D) 0
(ii) (1 + tan θ + sec θ) (1 + cot θ − cosec θ)
(A) 0
(B) 1
(C) 2
(D) −1
(iii) (secA + tanA) (1 − sinA) =
(A) secA
(B) sinA
(C) cosecA
(D) cosA
(iv)
(A) sec2 A
(B) −1
(C) cot2 A
(D) tan2 A
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Answer :
(i) 9 sec2A − 9 tan
2A
= 9 (sec2A − tan
2A)
= 9 (1) [As sec2 A − tan
2 A = 1]
= 9
Hence, alternative (B) is correct.
(ii)
(1 + tan θ + sec θ) (1 + cot θ − cosec θ)
Hence, alternative (C) is correct.
(iii) (secA + tanA) (1 − sinA)
= cosA
Hence, alternative (D) is correct.
(iv)
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Hence, alternative (D) is correct.
Question 5:
Prove the following identities, where the angles involved are acute angles for which the
expressions are defined.
Answer :
(i)
(ii)
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= secθ cosec θ +
= R.H.S.
(iv)
= R.H.S
(v)
Using the identity cosec2
= 1 + cot2
,
L.H.S =
Class:X Mathematics
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= cosec A + cot A
= R.H.S
(vi)
(vii)
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Hence, L.H.S = R.H.S
(x)
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