If tan x/2 = √(1 - e)/(1 + e) tan α/2, then cos α

Question

If tan\(\frac{x}{2}\) = \(\sqrt{\frac{1-e}{1+e}}\) tan\(\frac{\alpha}{2},\) then cos α =

A. 1 – e cos (cos x + e)

B. \(\frac{\text{1 + e cos x}}{\text{cos x - e}}\)

C. \(\frac{\text{1 - e cos x}}{\text{cos x - e}}\)

D. \(\frac{\text{cos x - e}}{\text{1 - e cos x}}\)

Answer 1

Correct answer is D.

By using the expansion of cos 2x in terms of tan x

Dividing the numerator and denominator by 1 + tan²\(\frac{\text{x}}{2}\)

[using the formula for cos 2x in terms of tan x