Prove that `tan^(-1)((cosx-sinx)/(cosx+sinx))=(pi/4-x), x lt pi`.

Explanation

To prove that

\[ \tan^{-1}\left(\frac{\cos x - \sin x}{\cos x + \sin x}\right) = \frac{\pi}{4} - x, \quad \text{for } x < \pi, \]

we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

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