Prove that the function given by $f(x) = \cos x$ is decreasing in $(0, \pi)$.

(N/A) Given the function $f(x) = \cos x$.
To determine the intervals of increase or decrease,we find the derivative $f'(x)$.
$f'(x) = \frac{d}{dx}(\cos x) = -\sin x$.
For the function to be decreasing,we require $f'(x) < 0$.
In the interval $(0, \pi)$,the value of $\sin x$ is always positive (i.e.,$\sin x > 0$).
Therefore,$f'(x) = -\sin x < 0$ for all $x \in (0, \pi)$.
Since the derivative is negative throughout the interval $(0, \pi)$,the function $f(x) = \cos x$ is strictly decreasing in $(0, \pi)$.