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Question
Prove the following identity :
`sec^2A.cosec^2A = tan^2A + cot^2A + 2`
Solution
LHS = `sec^2A.cosec^2A = 1/(cos^2A.sin^2A)`
RHS = `tan^2A + cot^2A + 2 = tan^2A + cot^2A + 2tan^2A.cot^2A`
= `(tanA + cotA)^2 = (sinA/cosA + cosA/sinA)^2`
= `((sin^2A + cos^2A)/(sinA.cosA))^2 = 1/(cos^2A.sin^2A)`
= Hence , LHS = RHS
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