A) \[\sec A+\tan A\]
B) \[\tan \left( \frac{\pi }{4}-A \right)\]
C) \[\tan \left( \frac{\pi }{4}+\frac{A}{2} \right)\]
D) \[\tan \left( \frac{\pi }{4}-\frac{A}{2} \right)\]
Correct Answer: D
Solution :
\[\sqrt{\frac{1-\sin A}{1+\sin A}}=\sqrt{\frac{1-\cos \left( \frac{\pi }{2}-A \right)}{1+\cos \left( \frac{\pi }{2}-A \right)}}\] \[=\sqrt{\frac{2{{\sin }^{2}}\left( \frac{\pi }{4}-\frac{A}{2} \right)}{2{{\cos }^{2}}\left( \frac{\pi }{4}-\frac{A}{2} \right)}}=\tan \left( \frac{\pi }{4}-\frac{A}{2} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
