Swetha and her friends went on vacation. They are staying in a cottage. The roof of the cottage was triangular in shape. Swetha and her friends are taking pictures in front of the cottage.

Based on the above information, solve the following questions:
1. If \(D\) is the mid-point of \(AC\), then find \(BD\).
2. Find \(\angle A\).
3. Find the value of \(1 - \cos^2 A\).
4. \(1 + tan^2 A = \)