Решить уравнение:tgx-3ctgx=0

[latex]tgx- \frac{3}{tgx}=0 [/latex] [latex]\frac{tg^{2}x-3}{tgx}=0[/latex] [latex] \left \{ {{tg^{2}x-3=0} \atop {tgx \neq 0}} \right. [/latex] [latex] \left \{ {{tg^{2}x=3} \atop {x \neq \pi k }} \right. [/latex] [latex] \left \{ {{tgx=+-\sqrt{3}} \atop {x \neq \pi k }} \right. [/latex] [latex]tgx=\sqrt{3}[/latex] [latex]x= \frac{ \pi }{3}+ \pi k [/latex], k∈Z [latex]tgx=-\sqrt{3}[/latex] [latex]x=- \frac{ \pi }{3}+ \pi k [/latex], k∈Z Ответ: [latex]x=+- \frac{ \pi }{3}+ \pi k [/latex], k∈Z