This is another homework problem:

Where do I begin? The problem states: Show that in (5.2) the average value of sin(mx)sin(nx) and of cos(mx)cos(nx), m does not equal n, are zero (over a period), by using the complex exponential forms for the sines and cosines as in (5.3).

I have attached the equations being referenced from the book. I really don't have a good idea where to start. I'm thinking I should start with Euler's identity but I don't know what to do here.