prove that cosec○(1+cos○)(cosec○-cot○)=1
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LHS=(cosecθ)(1+cosθ)(cosecθ−cotθ)
=(1/sinθ)(1+cosθ)[(1/sinθ)−(cosθ/sinθ)]
=(1/sinθ)(1+cosθ)[(1−cosθ)/sinθ]
=(1−cos²θ)/sin²θ
=sin²θ/sin²θ
=1=RHS
Hence, proved
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