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Question
Prove the following identity :
`cosec^4A - cosec^2A = cot^4A + cot^2A`
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Solution
LHS = `cosec^4A - cosec^2A`
= `cosec^2A(cosec^2A - 1)`
RHS = `cot^4A + cot^2A`
= `cot^2A(cot^2A + 1)`
= `(cosec^2A - 1)cosec^2A`
Thus , LHS = RHS
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