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

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

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

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

If sqrt(a + b) tan = theta/2 = sqrt(a -b) tan phi/2 then prove that a + b cos phi = (a cos phi+ b) sec theta .

If tan theta=1/2 and tan phi=1/3, then tan(2 theta+phi)

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

If tan^(2)theta=1+2tan^(2)phi then show that cos2 theta+sin^(2)phi=0

If tan^(2)theta=2tan^(2)phi+1, then cos2 theta+sin^(2)phi is equal to

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 .