Prove that `cos 4theta–cos 4alpha = 8(cos theta-cos alpha)(cos theta+ cos alpha )(cos theta -sin alpha)(cos theta+sin alpha)`

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

Prove that : cos^3 2theta+3cos2theta=4(cos^6theta-sin^6 theta)

Prove that (cos^3theta+sin^3 theta)/(cos theta+sin theta)+(cos^3 theta-sin^3 theta)/(cos theta-sin theta)=2

Under rotation of axes through theta , x cosalpha + ysinalpha=P changes to Xcos beta + Y sin beta=P then . (a) cos beta = cos (alpha - theta) (b) cos alpha= cos( beta - theta) (c) sin beta = sin (alpha - theta) (d) sin alpha = sin ( beta - theta)

Prove that: cos^2theta=cos^2alpha then theta=npi+-alpha,n in Z

If cos theta=(cos alpha-cos beta)/(1-cos alpha cos beta), prove that tan theta/2=+-tan alpha/2 cot beta/2.

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).

1 + (cos 2 theta + cos 6 theta)/(cos 4 theta) = (sin 3 theta)/(sin theta).

Show that cos^2theta+cos^2(alpha+theta)-2cosalphacostheta"cos"(alpha+theta) is independent of thetadot

If cos(theta - alpha) , costheta , cos(theta + alpha) are in H.P. then costheta.sec(alpha/2) =