If ` hat a` and ` hat b` are unit vectors inclined at an angle `theta` , then prove that `costheta/2=1/2| hat a+ hat b|` `tantheta/2=1/2|( hat a- hat b)/( hat a+ hat b)|`

Explanation

To prove the given statements, we will follow a step-by-step approach.

### Step 1: Find the Magnitude of \( \hat{a} + \hat{b} \)

We start with the expression for the magnitude of the sum of two vectors:

\[
|\hat{a} + \hat{b}|^2 = |\hat{a}|^2 + |\hat{b}|^2 + 2 \hat{a} \cdot \hat{b}
...