Show that the function f given by `f(x)=tan^(-1)(sinx+cosx),``x > 0`is always an strictly increasing function in `(0,pi/4)`.

Explanation

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

### Step 1: Define the function
Let \( g(x) = \sin x + \cos x \). We will analyze this function first, as \( f(x) \) is a composition of the increasing function \( \tan^{-1} \) and \( g(x) \).

### Step 2: Find the derivative of \( g(x) \)
To determine if \( g(x) \) is increasing, we need to find its derivative:
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