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Convert the following product into the sum or difference of sine and cosine:
$$\sin \frac{5 \pi}{12} \cos \frac{\pi}{12}$$
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## QuestionMathsClass 11

Convert the following product into the sum or difference of sine and cosine:
$$\sin \frac{5 \pi}{12} \cos \frac{\pi}{12}$$

$$\sin \frac{5 \pi}{12} \cos \frac{\pi}{12}=\frac{1}{2}\left(2 \sin \frac{5 \pi}{12} \cos \frac{\pi}{12}\right)$$
$$=\frac{1}{2}\left\{\sin \left(\frac{5 \pi}{12}+\frac{\pi}{12}\right)+\sin \left(\frac{5 \pi}{12}-\frac{\pi}{12}\right)\right\}$$ $$2 \sin x \cos y = \sin (x+y) + \sin (x-y)$$$$=\frac{1}{2}\left(\sin \frac{\pi}{2}+\sin \frac{\pi}{3}\right)$$