(1+cosecθ)(1−sinθ)=(cosθcotθ)
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L.H.S. = (1 – cos θ)/(1 + cos θ)
= (1 – cos θ)/(1 + cos θ) × (1 – cos θ)/(1 – cos θ)
= (1 – cos θ)2/(1 – cos2 θ)
= (1 – cos θ)2/sin2 θ
= [1 – cos θ/sin θ]2
= [1 /sin θ – cos θ/sin θ]2
= [cosec θ - cot θ]2
= [- (cot θ - cosec θ)]2
= (cot θ – cosec θ)2
= R.H.S.
Hence proved.
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