i've been doing integrals of trig functions because it's my weakest point.

there are a few basic things that i don't understand.

for eg. i KNOW that:

sin^2x=(1-Cos2x)/2

cos^2x=(1+Cos2x)/2

but please explain this, why is...

**1-(Cos^2)2x = 1-Cos4x**

and

**(Cos^3)2x = (1-(Sin^2)2x)Cos2x**