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

Explanation

To prove that the function \( f(x) = \log(\sin x) \) is strictly increasing on \( (0, \frac{\pi}{2}) \) and strictly decreasing on \( (\frac{\pi}{2}, \pi) \), we will analyze the derivative of the function.

### Step 1: Find the derivative of \( f(x) \)
The function is given by:
\[ f(x) = \log(\sin x) \]
To find the derivative \( f'(x) \), we use the chain rule:
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