If `cos^2 theta-sin theta=1/4`, then `theta=`

If cos^2 theta-sin^2 theta= 1/2 then cos^4 theta-sin^4 theta=?

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 .

If u = (1 + cos theta) (1+ cos2 theta) - sin theta sin 2theta, v = sin theta (1 + cos2 theta) + sin 2 theta(1 + cos theta), "show that" u^(2) + v^(2) = 4(1 + cos theta) (1 + cos 2theta).

(sin^(2) theta)/(1-cos theta)-(cos^(2) theta)/(1-sin theta)=cos theta-sin theta

If sin^(2)theta-cos^(2)theta=(1)/(4) , then the value of (sin^(4)theta-cos^(4)theta) is :

Prove that : sin theta cos^3 theta - cos theta sin^3 theta = 1/4 sin4theta .

Prove that sin theta cos^(3)theta - cos theta sin^(3) theta = (1)/(4) sin 4 theta .