If A = 3 4 , then 32 A 2 5 2 A = - Vidyadip

MCQ

If $\cos A = \frac{3}{4}$, then $32\sin \frac{A}{2}\cos \frac{5}{2}A = $

A
$\sqrt 7 $
✓
$ - \sqrt 7 $
C
$7$
D
$-7$

✓

Answer

Correct option: B.

$ - \sqrt 7 $

b
(b) $\cos A = \frac{3}{4} \Rightarrow \sin A = \frac{{\sqrt 7 }}{4}$

$L.H.S.$ $ = 16(\sin 3A - \sin 2A)$

$ = 16\sin A(3 - 4{\sin ^2}A - 2\cos A)$

$ = 16.\frac{{\sqrt 7 }}{4}\left( {3 - 4.\frac{7}{{16}} - 2.\frac{3}{4}} \right) = - \sqrt 7 $.

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