The general solution of the equation $$2cot$$θ$$2=1+$$$$cot$$θ$$2$$ is

Correct option is 3nπ+−1nπ6,n∈Z

Questions

The general solution of the equation $2 \cot \frac{θ}{2} = {(1 + \cot θ)}^{2}$ is

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nπ+−1nπ4,n∈Z

nπ+−1nπ3,n∈Z

nπ+−1nπ6,n∈Z

nπ2

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detailed solution

Correct option is C

We have 2cotθ2=1+cotθ2⇒2×2cosθ2×cosθ22sinθ2×cosθ2=1+cotθ2⇒21+cosθsinθ=cosec2θ+2cotθ ⇒2cosecθ+2cotθ=cosec2θ+2cotθ⇒cosecθ=2⇒sinθ=12⇒θ=nπ+−1nπ6,n∈Z

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The general solution of the equation 2cotθ2=1+cotθ2 is

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The general solution of the equation $2 \cot \frac{θ}{2} = {(1 + \cot θ)}^{2}$ is