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The value of (1−cos⁡θ)(1+cos⁡θ)\sqrt{\frac{(1-cos⁡θ)}{(1+cos⁡θ )}}(1+cos⁡θ)(1−cos⁡θ)​​​ is:
Question

The value of (1cosθ)(1+cosθ)\sqrt{\frac{(1-cos⁡θ)}{(1+cos⁡θ )}}​ is:

A.

cosec θ+cot⁡θ

B.

sec⁡θ+cot⁡θ

C.

sec⁡θ-cot⁡θ

D.

cosec θ-cot⁡θ

Correct option is D

Given:

(1cosθ)(1+cosθ)\sqrt{\frac{(1-cos⁡θ)}{(1+cos⁡θ )}}  

Solution:

(1cosθ)(1+cosθ)×(1cosθ)(1cosθ)\sqrt{\frac{(1-cos⁡θ)}{(1+cos⁡θ )}\times\frac{(1- cos⁡θ)}{(1- cos⁡θ )}}        

(1cosθ)2(sin2θ)\sqrt\frac{(1-cos\theta)^2}{( sin^2\theta)}   

=  (1cosθ)sinθ\frac{(1-cos\theta)}{sin\theta}

cosecθcotθcosec\theta - cot\theta 


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