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Question

(​sin​θ-cosec​θ) (cos​θ-sec​θ) (tan​θ+cot​θ) = 1

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Solution

LHS = sin θ - cosec θcos θ - sec θtan θ + cot θ=sin θ - 1sin θcos θ - 1cos θsin θcos θ + cos θsin θ=sin2θ - 1sin θcos2θ - 1cos θsin2θ + cos2θsin θ . cos θ=-1 - sin2θsin θ × -1 - cos2θcos θ × 1sin θ . cos θ=cos2θsin θ × sin2θcos θ× 1sin θ . cos θ=sin2θ . cos2θsin2θ . cos2θ=1=RHS

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