Answer
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Work Step by Step
$LHS=\frac{csc\theta-1}{cot\theta}\times\frac{csc\theta+1}{csc\theta+1}=\frac{csc^2\theta-1}{cot\theta(csc\theta+1)}=\frac{cot^2\theta}{cot\theta(csc\theta+1)}=\frac{cot\theta}{csc\theta+1}=RHS$
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