If `tan(theta/2)=sqrt((a-b)/(a+b))tan(phi/2)` , prove that `cosalpha=(acosphi+b)/(a+b cosphi)`

If tantheta/2=sqrt((2-b)/(a+b))tanphi/2 , prove that cosalpha=(1cosphi+b)/(a+b cosphi)

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

If tan(alpha/2)=sqrt((a-b)/(a+b)) tan(beta/2) prove that cosalpha=(acosbeta+b)/(a+bcosbeta)

If "tan"(theta)/(2)=sqrt((a-b)/(a+b))"tan"(varphi)/(2) , prove that cos theta =(a cosvarphi+b)/(a+bcosvarphi) .

If tan""(theta)/(2)=sqrt((1-e)/(1+e))tan""(phi)/(2) . Then prove that cosphi=(costheta-e)/(1-ecostheta) .

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= sqrt((a-b)/(a+b))"tan"(A)/(2) and cos varphi =(b+ a cos A)/(a+ b cosA) , show that varphi = 2 theta .

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 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 tan theta tan phi=sqrt((a-b)/(a+b)) , prove that a-bcos 2theta)(a-b cos 2phi) is independent of theta and phi .