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

MCQ

If $cos A = {3\over 4} , $ then $32\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{5A}}{2}} \right) = $

A
$7$
B
$8$
✓
$11$
D
None of these

✓

Answer

Correct option: C.

$11$

c
(c) $32\sin \frac{A}{2}\sin \frac{{5A}}{2} = 16(\cos 2A - \cos 3A)$

$ = 16(2{\cos ^2}A - 1 - 4{\cos ^3}A + 3\cos A)$

$ = 16\left( {2 \times \frac{9}{{16}} - 1 - 4 \times \frac{{27}}{{64}} + 3 \times \frac{3}{4}} \right) = 11$.

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