Fourier series help please...

[robgb]

I have a quantum physics 2nd year undergraduate exam in a few weeks, I'm a complete beginner to fourier series, can anyone help explain how to answer this question please? Thanks, rob.

The question is here (http://mobilecrazy.net/fourier.jpg)

[turin]

For part (a), you use an identity for the integral of a product of two trigonometric functions over a whole number multiple of the period. This is called the orthogonality condition, or orthogonality integral.

For part (b), you use this result from part (a) and and the orthogonality idea to solve it.