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Question
Prove the following identity :
`(1 + cotA)^2 + (1 - cotA)^2 = 2cosec^2A`
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Solution
`(1 + cotA)^2 + (1 - cotA)^2`
= `1 + cot^2A + 2cotA + 1 + cot^2A - 2cotA`
= `2 + 2cot^2A = 2(1 + cot^2A)`
= `2cosec^2A`
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