If `A = [(0,-tan(alpha//2)),(tan(alpha//2),0)]` and `I` is a `2xx2` unit matrix, prove that `I+A=(I-A)[(cosalpha,-sinalpha),(sinalpha,cosalpha)]`

Explanation

To prove that \( I + A = (I - A) \begin{pmatrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \end{pmatrix} \), where \( A = \begin{pmatrix} 0 & -\tan(\alpha/2) \\ \tan(\alpha/2) & 0 \end{pmatrix} \) and \( I \) is the \( 2 \times 2 \) identity matrix, we will follow these steps:

### Step 1: Define the matrices
Let:
\[ A = \begin{pmatrix} 0 & -\tan(\alpha/2) \\ \tan(\alpha/2) & 0 \end{pmatrix} \]
\[
...