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Question
Prove the following identity :
cosecθ(1 + cosθ)(cosecθ - cotθ) = 1
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Solution
LHS = cosecθ(1 + cosθ)(cosecθ - cotθ)
= `1/sinθ(1 + cosθ)(1/sinθ - cosθ/sinθ)`
= `((1 + cosθ))/sinθ ((1-cosθ)/sinθ)`
= `(1 - cos^2θ)/sin^2θ = sin^2θ/sin^2θ = 1 = RHS`
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