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

Prove that (1 - cos 2 theta)/( sin 2 theta) = tan theta.

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

If 3 tan theta tan phi=1, then (cos (theta-phi))/(cos (theta+phi)) is

If 3 tan theta tan phi=1, then (cos (theta-phi))/(cos (theta+phi)) is

(sin (theta + phi))/( sin theta cos phi) = cot theta tan phi +1.

If cos(theta+phi)= mcos(theta-phi) , then prove that tan theta=(1-m)/(1+m)cotphi .

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

Prove that (cos theta-sintheta)/(cos theta+sintheta)=sec 2 theta-tan 2theta .

If determinant |cos(theta+phi) sin(theta+phi)cos2phi sin thetacostheta sinphi costheta sintheta cosphi | is a. positive b. independent of theta c. independent of phi d. none of these