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

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 tan^(2)theta=2tan^(2)phi+1, prove that cos2 theta+sin^(2)phi=0

If 3tan theta tan phi=1. Prove that 2cos(theta+phi)=cos(theta-phi)

A line makes angles theta,phi and psi with x,y,z axes respectively. Consider the following. 1. sin^2theta+sin^2phi=cos^2psi 2. cos^2theta+cos^2phi=sin^2psi 3. sin^2theta+cos2theta=cos^2psi Which of the above is/are correct ?

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

A line makes angles theta,phiand Psi with x,y,z axes respectively. Consider the following ltbRgt 1. sin^2theta+sin^2phi=cos^2Psi 2. cos^2theta+cos^2phi=sin^2Psi 3. sin^2theta+cos^2phi=cos^2Psi Which of the above is/are correct?

If 3tan theta tan phi=1, then prove that 2cos(theta+phi)+cos(theta-phi)=0

If tan^(2)theta=1+2tan^(2)phi, prove that cos2 phi=1+2cos2 theta

Prove that: cos2 theta*cos2 phi+cos^(2)(theta+phi)-cos^(2)(theta-phi)=cos(2 theta+2 phi)