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Question

Prove that
cos(3π2+θ)cos(2π+θ)[cot(3π2θ)+cot(2π+θ)]=1

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Solution

L.H.S

cos(3π2+θ)cos(2π+θ)[cot(3π2θ)+cot(2π+θ)]

We know that

cos(3π2+θ)=sinθ

cos(2π+θ)=cosθ

cot(3π2θ)=tanθ

cot(2π+θ)=cotθ

Therefore,

sinθcosθ(tanθ+cotθ)

sinθcosθ(sinθcosθ+cosθsinθ)

sinθcosθ(sin2θ+cos2θsinθcosθ)

sin2θ+cos2θ

1

Hence, this is the answer.


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