identities sum and differences

Ok now being only a couple days late for this due to some technacal difficulties with logging on to blogger for some reason i can now conribute my wise learnings, I keep trying to tell myself this anyways, in the form of two examples.

So hear is exhibit A using the identity Cos(a+b):

= Cos(A)* Cos(B) -Sin(A)*Sin(B)

= Cos(5x)*Cos(2x)-Sin(5x)*Sin(2x)

= Cos(5x+2x)

= Cos(7x)

And now for exhibit B which is like A in reverse and more specific:
Cos(75 degrees)
= Cos(45 degrees+ 30 degrees)
= Cos(45)*Cos(30)-Sin(45)*Sin(30)
= (sqr(2)/2) * (sqr(3)/2) - (Sqr(2)/2) * 1/2
= (sqr(6)/4) - (sqr(2)/4)
= (sqr(6)-sqr(2))/4

Well hope this helps someone