Show that `f(x)=tan^(-1)(sinx+cosx)` is an increasing function on the interval `(0,\ pi//4)` .

Explanation

To show that the function \( f(x) = \tan^{-1}(\sin x + \cos x) \) is an increasing function on the interval \( (0, \frac{\pi}{4}) \), we will follow these steps:

### Step 1: Differentiate the function
We start by differentiating the function \( f(x) \):
\[ f'(x) = \frac{d}{dx} \left( \tan^{-1}(\sin x + \cos x) \right) \]
Using the chain rule, we have:
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