Aus Online Mathematik Brückenkurs 1

Suppose that \displaystyle \cos x\ne 0, so that we can divide both sides by \displaystyle \cos x to obtain

\displaystyle \frac{\sin x}{\cos x} = \sqrt{3}\qquad\text{i.e.}\qquad \tan x = \sqrt{3}\,\textrm{.}

This equation has the solutions \displaystyle x = \pi/3+n\pi for all integers n.

If, on the other hand, \displaystyle \cos x=0, then \displaystyle \sin x = \pm 1 (draw a unit circle) and the equation cannot have such a solution.

Thus, the equation has the solutions

\displaystyle x = \frac{\pi}{3}+n\pi\qquad(n is an arbitrary integer).