Question

The number of point(s) of intersection of the functions $f\left(x\right)=-\tan x$ and $g\left(x\right)=\cot x\forall x\in (-2\pi ,2\pi )$ is:

• A. 0

Answer 1

The correct option is A 0
Given functions: $f\left(x\right)=-\tan x$ and $g\left(x\right)=\cot x\forall x\in (-2\pi ,2\pi ).$
For finding the number of solutions of $f\left(x\right)=-\tan x$ and $g\left(x\right)=\cot x,$ lets draw the graphs of both the function in a single plane and find the number of points of intersection.
Now, the graph of $\tan x$ can be drawn as:

Now, flipping the graph w.r.t x - axis will give the graph of $-\tan x$ as:

Similarly, drawing the graph of $\cot x$ we get:

Thus, the two functions don't intersect at any points.