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

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

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

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

Prove that (sin theta -cos theta+1 )/( sin theta + cos theta -1) =(1)/( sec theta -tan theta ) [use the identity sec ^(2) theta =1 +tan ^(2) theta ]

Prove that cos^(3)thetasin3theta+sin^(3)theta cos 3theta=(3)/(4)sin 4 theta .

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

Prove that cos 8 theta cos 2 theta = cos^(2) 5theta- sin^(2) 3 theta

Prove that sin (270^(@)-theta) sin (90^(@)-theta)-cos(270^(@)-theta) cos (90^(@)+theta)+1=0

(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=?