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 given problem step by step, we start with the equations provided:

1. **Given Equations**:
\[ \frac{\sin(\theta - \alpha)}{\sin(\theta - \beta)} = \frac{a}{b} \]
\[
\frac{\cos(\theta - \alpha)}{\cos(\theta - \beta)} = \frac{c}{d}
...