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If $\cos A=\frac{3}{4}$, then $32 \sin \frac{A}{2} \cos \frac{5}{2} A=$
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Verified Answer
The correct answer is:
$-\sqrt{7}$
$\begin{aligned}
\cos A & =\frac{3}{4} \Rightarrow \sin A=\frac{\sqrt{7}}{4} \\
\text { L.H.S } & =16(\sin 3 A-\sin 2 A) \\
& =16 \sin A\left(3-4 \sin ^2 A-2 \cos A\right) \\
& =16 \cdot \frac{\sqrt{7}}{4}\left(3-4 \cdot \frac{7}{16}-2 \cdot \frac{3}{4}\right)=-\sqrt{7}
\end{aligned}$
\cos A & =\frac{3}{4} \Rightarrow \sin A=\frac{\sqrt{7}}{4} \\
\text { L.H.S } & =16(\sin 3 A-\sin 2 A) \\
& =16 \sin A\left(3-4 \sin ^2 A-2 \cos A\right) \\
& =16 \cdot \frac{\sqrt{7}}{4}\left(3-4 \cdot \frac{7}{16}-2 \cdot \frac{3}{4}\right)=-\sqrt{7}
\end{aligned}$
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