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Question

If cosecθ+cotθ=m, show that m21m2+1=cosθ

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Solution

Given : cosecθ+cotθ=m
=(1+cosθ)/sinθ
m21(1+cos2θ+2cosθsin2θ
2(cos2θ+2cosθ)sin2θ
m21=cosθcos2(θ/2)sin2θ
m2+11+cos2θ+2cosθ+sin2θsin2θ
2(1+cosθ)sin2θ
4cos2(θ2)/sin2θ
(m21)m2+1[4cosθcos2(θ/2)/sin2θ]/4cos2(θ/2)/sin2θ]=cosθ
Hence proved

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