If `sintheta + sin^(2)theta = 1` , prove that `cos^(2)theta + cos^(4)theta = 1`

If sintheta+sin^2theta=1, then prove that cos^(12)theta+3cos^10theta+3cos^8theta+cos^6theta+2cos^4theta+2cos^2theta-2=1

If costheta + sin theta = sqrt2 cos theta , prove that cos theta - sin theta = sqrt2 sin theta .

If tan^(4)theta +tan^(2) theta = 1 , then the value of cos^(4)theta +cos^(2)theta 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^(100) theta - cos^(100) theta =1 , then theta is

If x sin^(3)theta + y cos^(3)theta = sintheta costheta and x sin theta = y cos theta , prove that x^(2) + y^(2) = 1.

If f(x)=|{:( sin^2 theta , cos^(2) theta , x),(cos^(2) theta , x , sin^(2) theta ),( x , sin^(2) theta , cos^2 theta ):}|, theta in (0,pi//2), then roots of f(x)=0 are

Prove that 2 (sin^(6)theta +cos^(6) theta ) - 3(sin^(4)theta +cos^(4) theta ) + 1 = 0

sin^(4) theta + cos ^(4) theta + 2sin^(2) theta cos ^(2) theta has value 1.