Prove that the function f given by `f(x) = log sin x" is increasing on "(0,pi/2)` and decreasing on `(pi/2,pi)`.

Explanation

To prove that the function \( f(x) = \log(\sin x) \) is increasing on the interval \( (0, \frac{\pi}{2}) \) and decreasing on the interval \( (\frac{\pi}{2}, \pi) \), we will follow these steps:

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

\[ f'(x) = \frac{d}{dx}[\log(\sin x)] \]
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