If `tan[theta/2]=sqrt[[1-e]/[1+e]]tan[phi/2]` then prove that `cosphi=[costheta-e]/[1-ecostheta]`

If tan[(theta)/(2)]=sqrt((1-e)/(1+e))tan[(phi)/(2)] then prove that cos phi=(cos theta-e)/(1-e cos theta)

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)/(2))=sqrt((1-e)/(1+e))tan((alpha)/(2)) then cos alpha=

If tan(theta)/(2)=sqrt((1-e)/(1+e))tan(alpha)/(2), then cos alpha=1-e cos(cos theta+e)(b)(1+e cos theta)/(cos theta-e)(c)(1-e cos theta)/(cos theta-e) (d) (cos theta-e)/(1-e cos theta)

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

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

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

prove that 1+tan theta tan2 theta=sec2 theta