Show that `sin^8 theta + cos^8theta = 1 +2 sin^4 theta cos^4 theta - 4 sin^2 theta cos^2theta`

Prove that : sin^8 theta- cos^8 theta= (sin^2 theta- cos^2 theta)(1-2 sin^2 theta cos^2 theta) .

sin^2theta+cos^2theta=1 .

Prove that sin^4theta-cos^4theta=sin^2theta-cos^2theta .

Prove that sin^4theta+cos^4theta=1-2sin^2thetacos^2theta .

Prove the following identity : cos^4 theta- sin^4 theta= cos^2 theta-sin^2 theta= 2 cos^2 theta-1=1-2 sin^2 theta .

Prove that sin^6theta+cos^6theta=1-3sin^2thetacos^2theta .

Prove that : cos2 theta= cos^2 theta-sin^2 theta=1-2 sin^2 theta= 2 cos^2 theta-1 .

If int (sin 3 theta + sin theta ) cos theta e ^(sin theta ) d theta = (A sin ^(3) theta + B cos ^(2) theta + C sin theta + D cos theta +E)e^(sin theta)+F, then:

Prove the following identity : sin^4 theta+ cos^4 theta= 1-2 sin^2 theta cos^2 theta .

Prove that : sin 2 theta= 2sin theta cos theta .