Question
If $cos A = {3\over 4} , $ then $32\sin \left( {\frac{A}{2}} \right)\sin \left( {\frac{{5A}}{2}} \right) = $
✓
Answer
c
(c) $32\sin \frac{A}{2}\sin \frac{{5A}}{2} = 16(\cos 2A - \cos 3A)$
(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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