Lösung 4.4:8b
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Version vom 15:19, 22. Okt. 2008
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). |
