If tan A `=a/b`, then find the value of `("a sin A- b cos A")/("a sin A + b cos A")`.

Explanation

To solve the problem, we need to find the value of \(\frac{a \sin A - b \cos A}{a \sin A + b \cos A}\) given that \(\tan A = \frac{a}{b}\).

### Step 1: Express \(\sin A\) and \(\cos A\) in terms of \(a\) and \(b\)
Since \(\tan A = \frac{a}{b}\), we can express \(\sin A\) and \(\cos A\) using the definitions of tangent:
\[ \sin A = \frac{a}{\sqrt{a^2 + b^2}}, \quad \cos A = \frac{b}{\sqrt{a^2 + b^2}} \]

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