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=?

The value of theta , lying between theta =0 and theta=(pi)/(2) and satisfying the equation . |{:(1+ cos^(2 ) theta , sin^(2) theta , 4 sin 4 theta ),(cos^(2) theta , 1+sin^2 theta , 4 sin 4 theta ),(cos^(2) theta , sin^(2) theta , 1+ 4 sin 4 theta ):}|=0 , is

The value of theta , lying between theta =0 and theta=(pi)/(2) and satisfying the equation . |{:(1+ cos^(2 ) theta , sin^(2) theta , 4 sin 4 theta ),(cos^(2) theta , 1+sin^2 theta , 4 sin 4 theta ),(cos^(2) theta , sin^(2) theta , 1+ 4 sin 4 theta ):}|=0 , is

If sin theta + sin^(2) theta =1 then cos^(4) theta + cos^(8) theta + 2 cos^(6) theta =

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 .

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 .