Question

Which of the following functions is decreasing on $\left(0,\frac{\pi }{2}\right)$?

• A. $\sin 2x$
• B. $\cos 3x$
• C. $\tan x$
• D. $\cos 2x$

Answer 1

The correct option is D

$\cos 2x$

Explanation for the correct option:

Plot the graph of $\cos 2x$

The Graph of $\cos 2x$ is,

The $\cos 2x$ curve is decreasing from $\left(0,\frac{\pi }{2}\right)$.

Explanation for the incorrect options:

Plot the graph of $\cos 3x,\sin 2x$ and $\tan x$

For option (a)

The Graph of $\cos 3x$ is,

The $\cos 3x$ curve is decreasing and increasing from $\left(0,\frac{\pi }{2}\right)$.

For option (b)

The Graph of $Sin2x$ is,

The $Sin2x$ curve is increasing and decreasing from $\left(0,\frac{\pi }{2}\right)$.

For option (c)

The graph of $\tan x$ is,

The $\tan x$ curve is increasing from $\left(0,\frac{\pi }{2}\right)$.

Hence $\cos 2x$ is the only function that is decreasing from $\left(0,\frac{\pi }{2}\right)$.

Therefore, the correct option is option (d).