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Question

Question: \(\sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}}\) equals...

1−sin⁡θ1+sin⁡θ\sqrt{\frac{1 - \sin\theta}{1 + \sin\theta}} equals

A

0

B

1

C

sec⁡θ−tan⁡θ\sec\theta - \tan\theta

D

sec⁡θ.tan⁡θ\sec\theta.\tan\theta

Answer

sec⁡θ−tan⁡θ\sec\theta - \tan\theta

Explanation

Solution

(1−sin⁡θ)2(1−sin⁡2θ)=1−sin⁡θcos⁡θ=sec⁡θ−tan⁡θ\sqrt{\frac{(1 - \sin\theta)^{2}}{(1 - \sin^{2}\theta)}} = \frac{1 - \sin\theta}{\cos\theta} = \sec\theta - \tan\theta.