Trigonometric Identities Question 353
Question: $ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}= $ (when x lies in IInd quadrant)
Options:
A) $ \sin \frac{x}{2} $
B) $ \tan \frac{x}{2} $
C) $ \sec \frac{x}{2} $
D) $ cosec\frac{x}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}=\frac{\cos \frac{x}{2}+\sin \frac{x}{2}+\sin \frac{x}{2}-\cos \frac{x}{2}}{\cos \frac{x}{2}+\sin \frac{x}{2}-\sin \frac{x}{2}+\cos \frac{x}{2}} $ $ =\tan \frac{x}{2} $ .
BETA
