Question

find all values of x in the interval [0,2π] that satisfy the equation, tan(x)-√3=0

Answer 1

Notice that
\[
\tan (\pi/3)= \sqrt 3
\]
Hence we have to solve
\[
\tan(x) = \tan (\pi/3)
\]

Answer 2

Look at
http://www.math.missouri.edu/escgi/mucgi-bin/trigidentities.cgi
to see that
\[
\tan(x) = \tan (\pi/3) \implies x=\frac \pi 3 + k \pi, \quad k=0,\pm1, \pm2 ,\pm3 \dots\\
x=\frac \pi 3 \\
x=\frac \pi 3 +\pi= \frac {4\pi}3
\]
Two solutions between 0 and \( 2 \pi\)