Show that `f(x)=sin x(1+cosx)` is maximum at `x=pi/3` in the interval `[0,pi]dot`

Explanation

To show that the function \( f(x) = \sin x (1 + \cos x) \) has a maximum at \( x = \frac{\pi}{3} \) in the interval \([0, \pi]\), we will follow these steps:

### Step 1: Find the derivative of the function
We start by differentiating \( f(x) \).

\[ f(x) = \sin x (1 + \cos x) \]
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