### Instruction: Compute $\cos 15^\circ.$.### Response: I don't know the exact value of $\cos 15^\circ,$ but I can try to express it in terms of some other angles that I do know.
One way to do that is to use the angle subtraction formula for cosine, which says that $\cos (A - B) = \cos A \cos B + \sin A \sin B.$
I want to find $\cos 15^\circ,$ so I need to choose two angles A and B such that $A - B = 15^\circ.$
A good choice might be $A = 45^\circ$ and $B = 30^\circ,$ because I know the values of $\cos 45^\circ,$ $\cos 30^\circ,$ $\sin 45^\circ,$ and $\sin 30^\circ.$