Let `(sin(theta-alpha))/("sin"(theta-beta))=a/b a n d(cos(theta-alpha))/("cos"(theta-beta))=c /d t h e n(a c+b d)/(a d+b c)=` (a)`cos(alpha-beta)` (b) `sin(alpha-beta)` `sin(alpha+beta)` (d) none of these

Explanation

To solve the problem, we start with the given equations:

1. \(\frac{\sin(\theta - \alpha)}{\sin(\theta - \beta)} = \frac{a}{b}\)
2. \(\frac{\cos(\theta - \alpha)}{\cos(\theta - \beta)} = \frac{c}{d}\)

We need to find the value of \(\frac{ac + bd}{ad + bc}\).

### Step 1: Express \(a\) and \(c\) in terms of \(b\) and \(d\)
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