If `tan^2 theta = 1+2 tan^2 phi`, prove that `cos 2 phi = 1 + 2 cos 2 theta`.

If t a n^2theta=2tan^2phi+1 , prove that cos2theta+sin^2phi=0.

If 3 tan theta tan phi=1 , then prove that 2 cos (theta+phi)=cos (theta-phi) .

Prove: tan^2thetacos^2theta=1-cos^2theta

If tan theta tan phi=sqrt((a-b)/(a+b)) , prove that a-bcos 2theta)(a-b cos 2phi) is independent of theta and phi .

If sin theta is G.M. of sin phi and cos phi, then prove that cos 2 theta = 2 cos ^(2) ((pi)/(4) + phi).

If sin 2theta+sin 2phi=1//2 and cos2theta+cos 2phi=3//2 , then cos^(2)(theta-phi)=

If phi be the exterior angle of a regular polygon of n sides and theta is any constant, then prove that costheta+cos(theta+phi)+cos(theta+2phi)+…+to n term =0

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

If theta-phi=pi/2, prove that, [(cos^2 theta,cos theta sin theta),(cos theta sin theta,sin^2 theta)] [(cos^2 phi,cos phi sin phi),(cos phi sin phi,sin^2 phi)]=0

If theta+phi+psi=2pi, prove that cos^2theta+cos^2phi+cos^2psi -2costheta cosphi cospsi=1