Which of the following functions is decreasing on(0, π/2)?

The correct option is cos x.

To determine which function is decreasing on the interval
$\left(0,\frac{\pi }{2}\right)$
, we can analyze the first derivative of the functions. Recall that a function $f\left(x\right)$ is strictly decreasing on an open interval if its derivative $f^{\prime }\left(x\right)$ is negative for all points in that interval.

Let us test the function:
$f\left(x\right)=\cos x$

1. Find the first derivative of the function:
$f^{\prime }\left(x\right)=\frac{d}{dx}\left(\cos x\right)=-\sin x$

2. Analyze the sign of the derivative in the given interval:
$x\in \left(0,\frac{\pi }{2}\right)$

In the first quadrant, where $x$ lies between $0$ and $\frac{\pi }{2}$, the sine function is strictly positive:
$\sin x>0$

3. Consequently, multiplying by $-1$ makes the derivative negative:
$f^{\prime }\left(x\right)=-\sin x<0$

Since the derivative is strictly negative for all $x$ in the interval
$\left(0,\frac{\pi }{2}\right)$
, the function $\cos x$ is decreasing on this interval.