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Use the supplied product-to-sum identities

Given 2cos⁡Acos⁡B=cos⁡(A+B)+cos⁡(A−B)2\cos A\cos B=\cos(A+B)+\cos(A-B) and 2cos⁡Asin⁡B=sin⁡(A+B)−sin⁡(A−B)2\cos A\sin B=\sin(A+B)-\sin(A-B), find (a) ∫cos⁡3xcos⁡x dx\int\cos3x\cos x\,dx; (b) ∫cos⁡4xsin⁡x dx\int\cos4x\sin x\,dx.

CJC · Lecture · Example 15

Use the exact supplied identity for each product; the second has a difference of sines.

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