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: Find the derivative \( f'(x) \)

To determine if \( f(x) \) is increasing, we need to calculate its derivative \( f'(x) \).

Using the chain rule, the derivative of \( \tan^{-1}(u) \) where \( u = \sin x + \cos x \) is given by:

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