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Question
Prove the following identities:
`((1 + tan^2A)cotA)/(cosec^2A) = tan A`
Solution
L.H.S. = `((1 + tan^2A)cotA)/(cosec^2A)`
= `(sec^2A cotA)/(cosec^2A` ...(∵ sec2 A = 1 + tan2 A)
= `(1/(cos^2A) xx (cosA)/(sinA))/(1/(sin^2A))`
= `(1/(cosA sinA))/(1/(sin^2A))`
= `sinA/cosA`
= tan A = R.H.S.
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