Derive the Product-to-Sum formula sin a cos B = [sin (a+B) + sin (a-B)]. ..... First, rewrite the term sin (a + B), using the Sum Formula for the sine function. sin (a + B) = Now, rewrite the term sin (a - B), using the Difference Formula for the sine function. sin (a - B) = 1 Next, substitute the resulting expressions into the expression (sin (a+ B) + sin (a- B)], for sin (a + B) and sin (a - B) respectively, and then simplify. 1 (sin (a+ B) + sin (a- B)] = || (Simplify your answer.) 2. (Simplify your answer.) %3D Therefore, the resulting formula is shown below. Therefore, the resulting formula is shown below. 1 sin a cos B=,[sin (a + B) + sin (a - B)]

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