Discuss the extremum of `f(x)=sinx(1+cosx),x in (0,pi/2)`

Explanation

To discuss the extremum of the function \( f(x) = \sin x (1 + \cos x) \) for \( x \) in the interval \( (0, \frac{\pi}{2}) \), we will follow these steps:

### Step 1: Find the first derivative \( f'(x) \)

Using the product rule, we differentiate \( f(x) \):
\[ f'(x) = \sin x \cdot \frac{d}{dx}(1 + \cos x) + (1 + \cos x) \cdot \frac{d}{dx}(\sin x) \]
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