I'm having trouble with this problem. I've tried rewriting things in about every way I know how to but I haven't arrived at an answer. I'd appreciate some help.

"Let be an inner product space and let be an orthonormal subset of . Prove that for any we have "

As a hint the book says to use the fact that can be written uniquely as where and , the orthogonal complement of W, and use the fact that for , orthogonal, .

Thanks for any help.