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

Answer

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