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(phi/2) ,then show that cos phi=(cos theta-e)/(1-ecos theta) .

if tan (theta/2)=sqrt((1-e)/(1+e)) tan (varphi/2) ,then prove that cos varphi=(costheta-e)/(I-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 tan ""(alpha )/(2) = sqrt ({(1 -e)/( 1 +e)}) tan ""(beta)/(2), Prove that cos beta = ( cos alpha - e )/( 1 - e cos alpha ).

If cos theta = ( cos phi -e)/( 1- e cos phi ) , show that tan ""(theta)/( 2) = +- sqrt((1+e)/( 1-e)) tan ""(phi)/(2)

If cos theta = (cos phi-e)/(1-e cos phi) , show that : tan frac (theta)(2)= +- sqrt((1+e)/(1-e)) tan frac (phi)(2) .

If cos theta=(cos alpha cos beta)/(1-sin alpha sin beta), prove that one value of tan (theta/2)=(tan (alpha/2)-tan (beta/2))/(1-tan (alpha/2) tan (beta/2)).

If cos theta=(cos alpha-cos beta)/(1-sin alpha sin beta), prove that one value of tan(theta)/(2)=(tan(alpha)/(2)-tan(beta)/(2))/(1-tan(alpha)/(2)-tan(beta)/(2))

If tan theta=(tan alpha+tan beta)/(1+tan alpha tan beta) then show that sin2 theta=(sin2 alpha+sin2 beta)/(1+sin2 alpha sin2 beta)