Product‐Sum and Sum‐Product Identities. The process of converting  products into sums can make a difference  . 

Integrate \( \int \! \sin 3x \cos 4x \, \mathrm{d}x.\) This problem may seem tough at first, but after using the product-to-sum trigonometric formula, this integral very quickly changes into a standard form .

Converting a sum of trig functions into a product. Write as and then using the triple and double angle formulas

 

Product to Sum

Product of Sum