Answer
The equation $c=tan~x$ has exactly four solutions in the interval $(-2\pi,2\pi]$
Work Step by Step
Suppose that $~~c~~$ is any number.
In the interval $(-2\pi,-\pi]$, there is exactly one value of $x$ such that $c = tan~x$
In the interval $(-\pi,0]$, there is exactly one value of $x$ such that $c = tan~x$
In the interval $(0,\pi]$, there is exactly one value of $x$ such that $c = tan~x$
In the interval $(\pi,2\pi]$, there is exactly one value of $x$ such that $c = tan~x$
Therefore, in the interval $(-2\pi,2\pi]$, there are exactly four values of $x$ such that $c = tan~x$
The equation $c=tan~x$ has exactly four solutions in the interval $(-2\pi,2\pi]$
