Trigonometric Identities Question 341
Question: $ \sqrt{\frac{1-\sin A}{1+\sin A}}= $
Options:
A) $ \sec A+\tan A $
B) $ \tan ( \frac{\pi }{4}-A ) $
C) $ \tan ( \frac{\pi }{4}+\frac{A}{2} ) $
D) $ \tan ( \frac{\pi }{4}-\frac{A}{2} ) $
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Answer:
Correct Answer: D
Solution:
$ \sqrt{\frac{1-\sin A}{1+\sin A}}=\sqrt{\frac{1-\cos ( \frac{\pi }{2}-A )}{1+\cos ( \frac{\pi }{2}-A )}} $ $ =\sqrt{\frac{2{{\sin }^{2}}( \frac{\pi }{4}-\frac{A}{2} )}{2{{\cos }^{2}}( \frac{\pi }{4}-\frac{A}{2} )}}=\tan ( \frac{\pi }{4}-\frac{A}{2} ) $ .
BETA
