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

cos^(2)theta+sin^(2)theta cos2 beta=cos^(2)beta+sin^(2)beta cos2 theta

Prove that :(cos theta-sin theta)/(cos theta+sin theta)=sec2 theta-tan2 theta

prove that- sin^2theta/cos^2theta+cos^2theta/sin^2theta=1/ (sin^2thetacos^2theta)-2

Prove each of the following identities : (sin theta + cos theta)/(sin theta - cos theta) + (sin theta - cos theta)/(sin theta + cos theta) = (2) /((sin^(2) theta - cos^(2) theta)) = (2) /((2sin^(2) theta -1))

Prove each of the following identities : (i) (sin theta - cos theta)/(sin theta + cos theta) + ( sin theta+ cos theta)/(sin theta - cos theta) = (2)/((2 sin^(2) theta -1)) (ii) (sin theta + cos theta ) /(sin theta - cos theta) + ( sin theta - cos theta) /(sin theta + cos theta) = (2) /((1- 2 cos^(2) theta))

2(cos theta+cos2 theta)+(1+2cos theta)sin2 theta=2sin theta

Prove that : (1+sin2 theta-cos 2theta)/(sin theta+cos theta)=2sin theta

Prove that (cos theta-sin theta)/(cos theta+sin theta)=sec2theta-tan2theta

Prove that cos theta =(cos alpha- cos beta)/(1 -cos alpha*cos beta) ⇔ tan theta/2 = pm tan alpha/2 *cot beta/2 .