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Question

Prove : 1+cot2θ1+tan2θ=(1+cotθ1+tanθ)2

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Solution

LHS=1+cot2θ1+tan2θ=cosec2θsec2θ=cot2θ
RHS=(1+cotθ1+tanθ)2=(sinθ+cosθsinθsinθ+cosθcosθ)2=cot2θ
LHS=RHS
Hence Proved

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