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Question

If m=(cosθsinθ) and n=(cosθ+sinθ) then show that mn+nm=21tan2θ

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Solution

m=cosθsinθ n=cosθsinθ
mn+nm=m+nmn
m+n=cosθsinθ+cosθ+sinθ=2cosθ
mn=(cosθsinθ)(cosθ+sinθ)
=cos2θsin2θ
=cos2θ
m+nmn=2cosθcos2θ=2cos2θcos2θsin2θ
=2  1cos2θsin2θcos2θ
mn+nm=21tan2θ

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