Product-to-Sum and Sum-to-Product Formulas

Product-to-Sum Formulas

Example Express the following product as a sum or difference: Solution

Text Example Express each of the following products as a sum or difference. a. sin 8x sin 3x b. sin 4x cos x Solution The product-to-sum formula that we are using is shown in each of the voice balloons. a. sin 8x sin 3x = 1/2[cos (8x - 3x) - cos(8x + 3x)] = 1/2(cos 5x - cos 11x) sin  sin  = 1/2 [cos( - ) - cos( + )] sin  cos  = 1/2[sin( + ) + sin( - )] b. sin 4x cos x = 1/2[sin (4x + x) + sin(4x - x)] = 1/2(sin 5x + sin 3x)

Sum-to-Product Formulas

Example Express the difference as a product: Solution

Example Express the sum as a product: Solution

Example Verify the following identity: Solution