The value of sin frac{5 pi}{12} sin frac{pi}{ | vedclass

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Question

(D) Given expression is $\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$.We use the trigonometric identity $2 \sin A \sin B = \cos(A - B) - \cos(A + B)$.Mu

Vedclass · Accepted Answer

$\frac{1}{4}$

Vedclass · Answer

(D) Given expression is $\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$.We use the trigonometric identity $2 \sin A \sin B = \cos(A - B) - \cos(A + B)$.Multiplying and dividing by $2$,we get:$\frac{1}{2} [2 \sin \frac{5 \pi}{12} \sin \frac{\pi}{12}]$$= \frac{1}{2} [\cos(\frac{5 \pi}{12} - \frac{\pi}{12}) - \cos(\frac{5 \pi}{12} + \frac{\pi}{12})]$$= \frac{1}{2} [\cos(\frac{4 \pi}{12}) - \cos(\frac{6 \pi}{12})]$$= \frac{1}{2} [\cos(\frac{\pi}{3}) - \cos(\frac{\pi}{2})]$Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$ and $\cos(\frac{\pi}{2}) = 0$,$= \frac{1}{2} [\frac{1}{2} - 0] = \frac{1}{4}$.

The value of $\sin \frac{5 \pi}{12} \sin \frac{\pi}{12}$ is

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