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Question
Prove that:
`(cot A - 1)/(2 - sec^2 A) = cot A/(1 + tan A)`
Solution
L.H.S. = `(cot A - 1)/(2 - sec^2A)`
= `(((1 - tan A))/tan A)/(1 + 1 - sec^2A)`
= `(((1 - tan A))/tan A)/(1 - tan^2A)`
= `(((1 - tan A))/(tan A))/((1 + tan A)(1 - tan A))`
= `(1/tan A)/(1 + tan A)`
= `cot A/(1 + tan A)` = R.H.S.
Hence proved.
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