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Question
Prove the following identities:
`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`
Solution
L.H.S. = `1/(1+cosA)+1/(1-cosA)`
= `(1 - cosA + 1 + cosA)/((1 + cosA)(1 - cosA))`
= `2/(1 - cos^2A)` ...(∵ 1 – cos2 A = sin2 A)
= `2/(sin^2A)`
= 2 cosec2 A = R.H.S.
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