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Question

{1(sec2θcos2θ)+1(cosec2θsin2θ)}(sin2θcos2θ)=1sin2θcos2θ2+sin2θcos2θ

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Solution

{1(sec2θcos2θ)+1(cosec2θsin2θ)}(sin2θcos2θ)

={cos2θ(1+cos2θ)sin2θ+sin2θ(1+sin2θ)cos2θ}(sin2θcos2θ)

={cos4θ+cos4θsin2θ+sin4θ+sin4θcos2θ(1+cos2θ)(1+sin2θ)}

={cos4θ+sin4θ+sin2θcos2θ(sin2θ+cos2θ)2+sin2θcos2θ}

=1sin2θcos2θ2+sin2θcos2θ


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