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

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

Prove that sin^(6)theta+cos^(6)theta+3sin^(2)thetacos^(2)theta=1

If cos theta+sin theta=sqrt(2)cos theta then prove that cos theta-sin theta=sqrt(2)sin theta

Solve 7 cos^(2) theta+3 sin^(2) theta=4 .

(sintheta+sin2theta)/(1+costheta+cos2theta)

Solve 7cos^2theta+3sin^2theta=4

Prove: sin^4 theta - cos^4theta = 1 - 2cos^2 theta

The value of 3(cos theta-sin theta)^(4)+6(sin theta+cos theta)^(2)+4 sin^(6) theta is where theta in ((pi)/(4),(pi)/(2)) (a) 13-4cos^(4) theta (b) 13-4cos^(6) theta (c) 13-4cos^(6) theta+ 2 sin^(4) theta cos^(2) theta (d) 13-4cos^(4) theta+ 2 sin^(4) theta cos^(2) theta

Solve cos theta+cos 2theta+cos 3theta=0 .

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