If `tantheta=(sinalpha-cosalpha)/(sinalpha+cosalpha)` then show that ` sinalpha+cosalpha=sqrt(2)costheta`.

Explanation

To prove that \( \sin \alpha + \cos \alpha = \sqrt{2} \cos \theta \) given that \( \tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha} \), we will follow these steps:

### Step 1: Start with the given equation
We have:
\[ \tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha} \]

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