If `alpha` and `beta` are distict roots of `acostheta+b sintheta=c ,` prove that `sin(alpha+beta)=(2a b)/(a^2+b^2)`

Explanation

To prove that \( \sin(\alpha + \beta) = \frac{2ab}{a^2 + b^2} \), given that \( \alpha \) and \( \beta \) are distinct roots of the equation \( a \cos \theta + b \sin \theta = c \), we can follow these steps:

### Step 1: Set up the equations for roots
Since \( \alpha \) and \( \beta \) are roots of the equation \( a \cos \theta + b \sin \theta = c \), we can write:
\[ a \cos \alpha + b \sin \alpha = c \quad \text{(1)} \]
\[
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