`sin^2theta-cos^2phi = sin^2phi-cos^2theta`

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 ?

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

if determinant |{:( cos (theta + phi),,-sin (theta+phi),,cos 2phi),(sin theta,,cos theta,,sin phi),(-cos theta,,sintheta,,cos phi):}| is

The value of the determinant ,cos(theta+phi),-sin(theta+phi),cos2 phisin theta,cos theta,sin phi-cos theta,sin theta,cos phi]| is

If sim 2theta+sin2phi=1/2 and cos 2theta+cos2phi=3/2 then cos^2(theta-phi)=

If theta-phi=pi/2, then show that [[cos^2theta,costhetasintheta],[costhetasintheta,sin^2theta]]*[[cos^2phi,cosphisinphi],[cosphisinphi,sin^2phi]]=0

The determinant |(cos(theta+phi),-sin(theta+phi),cos2phi),(sintheta,costheta,sinphi),(-costheta,sintheta,cosphi)| is

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