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Question

If U=cot1cos2θtan1cos2θ, then sinU is equal to

A
sin2θ
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B
cos2θ
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C
tan2θ
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D
tan22θ
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Solution

The correct option is B tan2θ
U=cot1cos2θtan1cos2θ
U=π2tan1cos2θtan1cos2θ
U=π22tan1cos2θ
U=π2tan1(2cos2θ1cos2θ)
U=π2tan1(cos2θsin2θ)
tan(π2U)=cos2θsin2θ
cotU=cos2θsin2θ
sinU=11+cot2θ=11+cosθsin4θ
sinU=sin2θsin4θ+12sin2θ
sinU=sin2θ1sin2θ=tan2θ

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