Prove that `sin^2 theta+sin^2 2theta+sin^2 3theta+....+sin^2 n theta=n/2-(sin n theta cos(n+1)theta)/(2sin theta)`

Prove that cos^6 theta+ sin^6 theta= 1-3sin^2 theta cos^2 theta

Prove that: sin theta- 1/2 sin 2 theta+1/3 sin 3theta-…to oo = theta/2

Using induction, prove that cos theta · cos 2theta · cos 2^2 theta. ... cos 2^(n-1) theta =(sin2^n theta)/(2^n sin theta)

Prove that : (sin theta + 2 sin 3theta + sin 5theta)/(sin 3theta + 2 sin 5theta + sin 7theta) = (sin 3theta)/(sin 5theta)

Prove that sintheta+sin3theta+sin5theta+.....+sin(2n-1)theta=(sin^2ntheta)/(sintheta)dot

Prove that (2 sin theta - sin 2theta)/(2 sin theta + sin 2theta) = tan^2\ theta/2

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

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

Prove that cos theta cos 2 theta cos 4 theta…. Cos 2 ^(n-1) theta = ( sin ( 2 ^(n) theta))/( 2 ^(n) (sin theta)) .

Prove that sintheta+s in3theta+sin5theta++sin(2n-1)theta=(sin^2ntheta)/(sintheta)dot