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

Explanation

To solve the equation \( \tan \theta = \frac{\sin \alpha - \cos \alpha}{\sin \alpha + \cos \alpha} \) and show that \( \sin \alpha + \cos \alpha = \sqrt{2} \cos \theta \), we will follow these steps:

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

...