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Question

Prove that : (1sinθ+cosθ)2=2(1+cosθ)(1sinθ)

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Solution

LHS=(1sinθ+cosθ)2

LHS=1+sin2θ+cos2θ2sinθ+2cosθ2sinθcosθ

LHS=22sinθ+2cosθ2sinθcosθ

LHS=2(1sinθ)+2cosθ(1sinθ)

LHS=2(1sinθ)(1+cosθ)=RHS

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