Simplify `tan^(-1)[(acosx-bsinx)/(bcosx+asinx)],`if `a/btanx > -1`.

Explanation

To simplify the expression \( \tan^{-1}\left(\frac{a \cos x - b \sin x}{b \cos x + a \sin x}\right) \) given that \( \frac{a}{b} \tan x > -1 \), we will follow these steps:

### Step 1: Divide the numerator and denominator by \( b \cos x \)

We start by rewriting the expression:

\[
\tan^{-1}\left(\frac{a \cos x - b \sin x}{b \cos x + a \sin x}\right) = \tan^{-1}\left(\frac{\frac{a \cos x}{b \cos x} - \frac{b \sin x}{b \cos x}}{\frac{b \cos x}{b \cos x} + \frac{a \sin x}{b \cos x}}\right)
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