What is the double angle formula?

The double angle formula is how to combine/split trigonometric functions so that they can be integrated or simplified using identities. For example, cos (a+b)= cos(a)cos(b) - sin(a)sin(b) , which can be extended to cos(2a)= cos^2(a)-sin^2(a). This is useful for instances where you are required to integrate/differentiate sin^2(x) for example, as using the identity cos^2(x)+sin^2(x)=1 means that the double angle formula can rearrange cos(2x) into 1-2sin^2(x),meaning that sin^2(x) =(cos(2x)-1)/2. This can be integrated with ease into sin(2x)/4 -x/2 +c.