Question

kn me lo puede resolver esto...
tg 3x-ctg 6x =0

Answer 1

$\text{Sea }z=3x\text{ entonces: }\\ \\ \tan z-\cot 2z = 0\\ \\ \displaystyle \tan z -\frac{1}{\tan 2z}=0\\ \\ \tan z -\frac{1-\tan^2z}{2\tan z}=0\\ \\ \frac{3\tan^2z-1}{2\tan z}=0\\ \\ 3\tan^2z-1=0 \wedge \tan z\neq 0\\ \\ \tan z =\pm\frac{1}{\sqrt{3}}$

$z_{principal}\in\{30\°;150\°\}\\ \\ z \in \{30\°+360\°k;150\°+360\°k\}\\ \\ z \in \{30\°+360\°k;-30\°+180\°(2k+1)\}\\ \\ z=(-1)^n\cdot 30\°+180\°\,n\;\; , n\in \mathbb Z\\ \\ \boxed{x=(-1)^n\cdot 10\°+60\°\,n\;\; , n\in \mathbb Z}$