If `alpha and beta` are roots of the equation `a cos theta + b sin theta = c`, then find the value of `tan (alpha + beta).`

Explanation

To find the value of \( \tan(\alpha + \beta) \) given that \( \alpha \) and \( \beta \) are the roots of the equation \( a \cos \theta + b \sin \theta = c \), we can follow these steps:

### Step 1: Rewrite the equation
Start with the equation:
\[ a \cos \theta + b \sin \theta = c \]
We divide the entire equation by \( \cos \theta \):
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