If `(sin(x+y))/(sin(x-y))=(a+b)/(a-b)` , show that `(tanx)/(tany)=a/b` .

Explanation

To prove that \(\frac{\tan x}{\tan y} = \frac{a}{b}\) given that \(\frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b}\), we can follow these steps:

### Step 1: Start with the given equation
We have:
\[ \frac{\sin(x+y)}{\sin(x-y)} = \frac{a+b}{a-b} \]

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