Show that the function given by `f (x) = sinx` is
(a) strictly increasing in `(0,pi/2)` (b) strictly decreasing in `(pi/2,pi)`(c) neither increasing nor decreasing in `(0, pi)`

Explanation

To show that the function \( f(x) = \sin x \) is strictly increasing in \( (0, \frac{\pi}{2}) \), strictly decreasing in \( (\frac{\pi}{2}, \pi) \), and neither increasing nor decreasing in \( (0, \pi) \), we will follow these steps:

### Step 1: Find the derivative of \( f(x) \)
The first step is to differentiate the function \( f(x) = \sin x \).

\[ f'(x) = \cos x \]
...