Getting exact answer from cos(u+-v) & sin(u+-v). Simple problem.

Having a simple problem again.

First: I'm really sorry, I've looked and I can't find and post on how to insert the correct "Math-Code" (well, I don't know how to insert degrees, square root and other things).

* = degrees

Example:

Determine the EXACT value of cos(15*) by rewriting cos(15*) = cos(45*-30*):

I can get exact values like:

cos15* = cos(45*-30*) = cos45*cos30* + sin45*sin30* = 0.965925......

But, ofcourse, this won't do. The correct answer is:

(squareroot(6) + squareroot(2))/4

How can I get the correct (well, I guess both are correct if I write the whole answer, but I mean the "better looking" one) later answer instead of the first? Appreciate help!!