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Question

Show that (cosecΘcotΘ)2=1cosΘ1+cosΘ

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Solution

LHS=(cosecθcotθ)2=(1sinθcosθsinθ)2=(1cosθ)2sin2θ=(1cosθ)21cos2θ=(1cosθ)2(1cosθ)(1+cosθ)=1cosθ1+cosθ=RHS

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