1+ A- A 1+ A+ A = - Vidyadip

MCQ

$\frac{1+\sin A-\cos A}{1+\sin A+\cos A}=$

A
$\sin \frac{A}{2}$
B
$\cos \frac{ A }{2}$
✓
$\tan \frac{A}{2}$
D
$\cot \frac{ A }{2}$

✓

Answer

Correct option: C.

$\tan \frac{A}{2}$

(C)
$\frac{1+\sin A -\cos A }{1+\sin A +\cos A }=\frac{2 \sin ^2 \frac{A}{2}+2 \sin \frac{A}{2} \cos \frac{A}{2}}{2 \cos ^2 \frac{A}{2}+2 \sin \frac{A}{2} \cos \frac{A}{2}}$
$=\frac{2 \sin \frac{A}{2}\left(\sin \frac{A}{2}+\cos \frac{ A }{2}\right)}{2 \cos \frac{A}{2}\left(\cos \frac{A}{2}+\sin \frac{ A }{2}\right)}$
$=\tan \frac{ A }{2}$

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