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Prove-csc^2x=cos^2x+cot^2x+sin^2x

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Answer:

Recall the following identities

cos2α+sin2α=1

cot2β+1=csc2β

Hence,

cot2(2x)+cos2(2x)+sin2(2x)=cot2(2x)+(cos2(2x)+sin2(2x))=1cot2(2x)+1=csc2(2x)

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