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# Question and Answer

Convert each of the following products into the sum or differences of sines and cosines : $$\cos \frac{5 \pi}{12} \cos \frac{\pi}{12}$$
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## QuestionMathsClass 11

Convert each of the following products into the sum or differences of sines and cosines : $$\cos \frac{5 \pi}{12} \cos \frac{\pi}{12}$$

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