If `t a ntheta/2=sqrt((1-e)/(1+e))tan(alpha/2)`, then `cosalpha=`
(a) `1-ecos(costheta+e)`
(b) `(1+ecostheta)/(costheta-e)`
(c) `(1-ecostheta)/(costheta-e)`
(d) `(costheta-e)/(1-ecostheta)`

Explanation

To solve the equation \( \frac{\tan \theta}{2} = \sqrt{\frac{1-e}{1+e}} \tan \frac{\alpha}{2} \) and find \( \cos \alpha \), we can follow these steps:

### Step 1: Square both sides
We start with the given equation:
\[ \tan \frac{\theta}{2} = \sqrt{\frac{1-e}{1+e}} \tan \frac{\alpha}{2} \]
Squaring both sides gives:
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