( 2A 1 + 2A ) , ( A 1 + A )= - Vidyadip

MCQ

$\left( {\frac{{\sin 2A}}{{1 + \cos 2A}}} \right)\,\left( {\frac{{\cos A}}{{1 + \cos A}}} \right)= $

✓
$\tan \frac{A}{2}$
B
$\cot \frac{A}{2}$
C
$\sec \frac{A}{2}$
D
${\rm{cosec}}\frac{A}{2}$

✓

Answer

Correct option: A.

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

a
(a) $\left( {\frac{{\sin 2A}}{{1 + \cos 2A}}} \right)\,\left( {\frac{{\cos A}}{{1 + \cos A}}} \right)$

$ = \frac{{2\sin A\cos A}}{{2{{\cos }^2}A}}\frac{{\cos A}}{{1 + \cos A}}$

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

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

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