Find the number of solution of the equation `sqrt(cos 2x+2)=(sin x + cos x)` in `[0, pi]`.

Explanation

To find the number of solutions for the equation \( \sqrt{\cos(2x) + 2} = \sin(x) + \cos(x) \) in the interval \( [0, \pi] \), we will follow these steps:

### Step 1: Square both sides
We start with the equation:
\[ \sqrt{\cos(2x) + 2} = \sin(x) + \cos(x) \]
Squaring both sides, we get:
...