Prove that: `(costheta)/(1+sintheta)=tan(pi/4-theta/2)`

Explanation

To prove that \(\frac{\cos \theta}{1 + \sin \theta} = \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right)\), we will start with the left-hand side and manipulate it step by step.

### Step 1: Rewrite \(\cos \theta\) and \(\sin \theta\) using half-angle identities
We know that:
\[ \cos \theta = \cos(2 \cdot \frac{\theta}{2}) = \cos^2\left(\frac{\theta}{2}\right) - \sin^2\left(\frac{\theta}{2}\right) \]
and
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