Given that `(1+tan1^@)(1+tan2^@)...........(1+tan45^@)= 2^n `find n .

Explanation

To solve the problem, we need to evaluate the expression \((1 + \tan 1^\circ)(1 + \tan 2^\circ)(1 + \tan 3^\circ) \ldots (1 + \tan 45^\circ)\) and express it in the form \(2^n\).

### Step-by-Step Solution:

1. **Understanding the Expression**:
We need to compute the product:
\[
P = (1 + \tan 1^\circ)(1 + \tan 2^\circ)(1 + \tan 3^\circ) \ldots (1 + \tan 45^\circ)
...