Prove that : `cos^2 theta + sin^2 theta cos 2 beta = cos^2 beta + sin^2 beta cos 2theta`

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

Prove that ( cos theta + cos 2 theta + cos 3 theta + cos 4 theta)/(sin theta + sin 2 theta + sin 3 theta + sin 4 theta)= cot ""(5theta)/(2).

Prove that : (cos 4theta + cos 3theta + cos 2theta)/(sin 4theta + sin 3theta + sin 2theta) = cot 3theta

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)) .

cos ^(2) 2 theta - sin ^(2) theta = cos theta . cos 3 theta.

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

If f (theta) = [[cos^(2) theta , cos theta sin theta,-sin theta],[cos theta sin theta , sin^(2) theta , cos theta ],[sin theta ,-cos theta , 0]] ,then f ( pi / 7) is

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