If π<θ<$$2$$π, then $$1+$$$$cos$$⁡θ$$1$$−$$cos$$⁡θ is equal to

Correct option is 4−cosec⁡θ−cot⁡θ

Questions

If $π < θ < 2 π$ , then $\sqrt{\frac{1 + \cos θ}{1 - \cos θ}}$ is equal to

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cosec⁡θ+cot⁡θ

cosec⁡θ−cot⁡θ

−cosec⁡θ+cot⁡θ

−cosec⁡θ−cot⁡θ

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detailed solution

Correct option is D

we have,1+cos⁡θ1−cos⁡θ=(1+cos⁡θ)21−cos2⁡θ⇒ 1+cos⁡θ1−cos⁡θ=1+cos⁡θ|sin⁡θ|⇒ 1+cos⁡θ1−cos⁡θ=1+cos⁡θ−sin⁡θ [∵π<θ<2π⇒sin⁡θ<0]⇒ 1+cos⁡θ1−cos⁡θ=−cosec⁡θ−cot⁡θ

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If π<θ<2π, then 1+cos⁡θ1−cos⁡θ is equal to

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If $π < θ < 2 π$ , then $\sqrt{\frac{1 + \cos θ}{1 - \cos θ}}$ is equal to