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Question
Prove the following identities:
(cosec A + sin A) (cosec A – sin A) = cot2 A + cos2 A
Solution
L.H.S. = (cosec A + sin A) (cosec A – sin A)
= (cosec2 A – sin2 A) ...[∵ (a + b) (a – b) = a2 – b2]
= 1 + cot2 A – sin2 A
= cot2 A + 1 – sin2 A
= cot2 A + cos2 A ...(∵ 1 – sin2 A = cos2 A)
= R.H.S.
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