Chapter 6.3, Problem 118E

Exercises 116-118 will help you prepare for the material covered in the next section. In each exercise, use exact values of trigonometric functions to show that the statement is true. Notice that each statement expresses the product of sines and/or cosines as a sum or a difference.

$\sin \pi \cos \frac{\pi }{3}=\frac{1}{2}\left[\sin \left(\pi +\frac{\pi }{2}\right)+\sin \left(\pi -\frac{\pi }{2}\right)\right]$