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Question
Prove the following trigonometric identity.
`cos^2 A + 1/(1 + cot^2 A) = 1`
Solution
L.H.S. = `cos^2 A + 1/(1 + cot^2 A)`
= `cos^2 A + 1/("cosec"^2 A) ...[1 + cot^2A = "cosec"^2 A]`
= `cos^2 A + sin^2 A ...[1/("cosec" A) = sin A]`
= `cos^2 A + sin^2 A`
= 1 (R.H.S.) ...`[sin^2 A + cos^2A = 1]`
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