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Question

Prove that:

cosθ(1tanθ)sin2θ(cosθsinθ)=(cosθ+sinθ)

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Solution

cosθ(1tanθ)sin2θ(cosθsinθ)

=cosθ1sinθcosθsin2θcosθsinθ

=cos2θcosθsinθsin2θcosθsinθ

=cos2θsin2θcosθsinθ

=(cosθsinθ)(cosθ+sinθ)cosθsinθ

=cosθ+sinθ


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