Question

If tan theta/2 = root of 1-e/1+e tan phi/2 prove that cos phi = cos theta - e/ 1- e cos theta

Answer 1

tanθ/2=√(1-e)/(1+e) tanФ/2
or, tanФ/2=√(1+e)/(1-e) tanθ/2
squaring both sides, 
tan²Ф/2=(1+e)/(1-e) tan²θ/2
or, (1-tan²Ф/2)/(1+tan²Ф/2)={(1-e)-(1+e)tan²θ/2}/{(1-e)+(1+e)tan²θ/2}
[by dividendo-componendo method]
or, cosФ=(1-e-tan²θ/2-etan²θ/2)/(1-e+tan²θ/2+etan²θ/2)
or, cosФ={(1-tan²θ/2)-e(1+tan²θ/2)}/{(1+tan²θ/2)-e(1-tan²θ/2)}
or, cosФ=[{(1-tan²θ/2)-e(1+tan²θ/2)}/(1+tan²θ/2)]/
                                                   [{(1+tan²θ/2)-e(1-tan²θ/2)}/(1+tan²θ/2)]
or, cosФ=(cosθ-e)/(1-ecosθ) [∵, (1-tan²θ/2)/(1+tan²θ/2)=cosθ] (Proved)

Answer 2

Answer is in the attachment. please mark as brainliest.