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Question

Prove that : (sinθ+secθ)2+(cosθ+cosecθ)2=(1+secθcosecθ)2.

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Solution

(sinθ+secθ)2+(cosθ+cosecθ)2=(1+cosecθ.secθ)2

=sin2θ+2sinθ.secθ+cos2θ+cosec2θ+2cosθ.cosecθ

=1+sec2θ+cosec2θ+2secθcosecθ+cosecθsecθ

=1+sec2θ+cosec2θ+2cosecθ.secθ

=(1+cosecθ.secθ)2

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