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Question

Show that 1+tan2θ1+cot2θ=(1tanθ1cotθ)2=tan2θ

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Solution

LHS=(1tanθ1cotθ)2=(1sinθcosθ)2(1cosθsinθ)2
=(cosθsinθ)2sin2θcos2θ(sinθcosθ)2
=tan2θ=RHS
LHS=RHS
Hence proved.

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