Use the principle of mathematical induction to prove that for all `n in N`
`sqrt(2+sqrt(2+sqrt2+...+...+sqrt2))=2cos ((pi)/(2^(n+1)))`
When the LHS contains n radical signs.

Explanation

To prove the statement using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We need to verify the statement for \( n = 1 \).

**Left-Hand Side (LHS)**:
\[
\sqrt{2} = 2 \cos\left(\frac{\pi}{2^{1+1}}\right) = 2 \cos\left(\frac{\pi}{4}\right) = 2 \cdot \frac{1}{\sqrt{2}} = \sqrt{2}
...