First use the identity
= ,
which gives you
= .
Therefore, the left side of the given hypothetical identity becomes
- = - . (1)
Next, use the trigonometric identity
cos(a)*cos(b) - sin(a)*sin(b) = cos(a+b).
It allows you to continue the line (1) in this way
- = - = = .
Thus
- = .
It is what has to be proved.
