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

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

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

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

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

cos2thetacos2phi+sin^2(theta-phi)-sin^2(theta+phi)=

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

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

If theta = (pi)/(2 ^(n) +1) prove that 2 ^(n) cos theta cos 2 theta cos 2 ^(2) theta…. Cos 2 ^(n -1) theta =1