Question

Consider the information given below
I. Domain of $\tan x$ is
$R^{+}-\left\{(2 n+1) \frac{\pi}{2}: n \in Z\right\}$
II. Range of $\tan x$ is $R$.
III. Graph of $\tan x$ repeats after an interval of $\pi$ i.e., $\tan (\pi+x)=\tan x$
Choose which among the following is correct.

• A. $\mid$ is correct
• B. II is correct
• C. II and III are correct
• D. All are correct

Answer 1

Answer: (C)

We have, seen that domain and range of $\tan x$ is $R-\left\{(2 n+1) \frac{\pi}{2}: n \in Z\right\}$ and $R$ respectively. Also, the following the behaviour of trigonometric function $\tan x$, we get the graph as shown below

Now, it can be understood that the graph of $\tan x$ repeats after an interval of $\pi$ i.e., $\tan (\pi+x)=\tan x$.