Solution 4.4:8b
From Förberedande kurs i matematik 1
Suppose that \displaystyle \text{cos }x\ne 0 , so that we can divide both sides by \displaystyle \text{cos }x to obtain
\displaystyle \frac{\sin x}{\cos x}=\sqrt{3}
i.e.
\displaystyle \tan x=\sqrt{3}
This equation has the solutions
\displaystyle x=\frac{\pi }{3}+n\pi
for all integers
\displaystyle n.
If, on the other hand, \displaystyle \text{cos }x=0, so \displaystyle \text{sin }x\text{ }=\pm \text{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
(
\displaystyle n
an arbitrary integer).
