If `theta=pi/(2^n+1)` , prove that: `2^ncosthetacos2thetacos2^2theta....... cos2^(n-1)theta=1.`

Prove that: (sin2theta)/(1-cos2theta)=cottheta

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

Prove that: (sin2theta)/(1+cos2theta)=tantheta

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

Prove that: cos^2 theta (1 + tan^2 theta) = 1

Prove that : (2 cos 2^n theta + 1)/(2 cos theta +1) = (2 cos theta -1) (2 cos 2theta -1) (2 cos 2^2 theta -1) … (2 cos 2^(n-1) theta -1)

Prove that cos theta +cos ((2pi)/(3)-theta)+cos ((2pi)/(3)+theta)=0

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

Prove that (sin theta+sin 2theta)/(1+cos theta+cos 2 theta)=tan theta

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