If `s inalpha+s inbeta=a\ a n d\ cosalpha+cosbeta=b ,` show that : `cos(alpha+beta)=(b^2-a^2)/(a^2+b^2)`

Explanation

To prove that \( \cos(\alpha + \beta) = \frac{b^2 - a^2}{a^2 + b^2} \) given that \( \sin \alpha + \sin \beta = a \) and \( \cos \alpha + \cos \beta = b \), we can follow these steps:

### Step 1: Square the equations
Starting with the given equations, we square both sides.

1. \( \sin \alpha + \sin \beta = a \)
\[
(\sin \alpha + \sin \beta)^2 = a^2
...