A) \[\sin \frac{A\text{ }}{2}\]
B) \[\cos \frac{A\text{ }}{2}\]
C) \[\tan \frac{A\text{ }}{2}\]
D) \[\cot \frac{A\text{ }}{2}\]
Correct Answer: C
Solution :
[c]:\[\frac{1+\sin A-\cos A}{1+\sin A+\cos A}\] \[=\frac{2{{\sin }^{2}}\frac{A}{2}+2sin\frac{A}{2}\cos \frac{A}{2}}{2{{\cos }^{2}}\frac{A}{2}+2\sin \frac{A}{2}\cos \frac{A}{2}}\] \[=\frac{2\sin \frac{A}{2}\left( sin\frac{A}{2}+\cos \frac{A}{2} \right)}{2\cos \frac{A}{2}\left( \cos \frac{A}{2}+sin\frac{A}{2} \right)}=\tan \frac{A}{2}\]
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