Помогите решить уравнение tgx/2+tgx/3=0

sin x/2/cosx/2+sinx/3/cosx/3=[(sinx/2*cosx/3+sinx/3*cosx/2]/(c0sx/2*cosx/3)= = sin(x/2+x/3)/(cosx/2*cosx/3)=0 x/2+x/3=5x/6=πk   k∈Z   x=6πk/5

[latex]tgx+tgy= \frac{sin(x+y)}{cosxcosy} [/latex] [latex]tg \frac{x}{2} +tg \frac{x}{3} =0[/latex] [latex] \frac{sin( \frac{x}{2} + \frac{x}{3}) }{cos \frac{x}{2}cos \frac{x}{3} } =0[/latex] ОДЗ: [latex]cos \frac{x}{2} \neq 0[/latex] [latex]cos \frac{x}{3} \neq 0[/latex] [latex] \frac{x}{2} \neq \frac{ \pi }{2} + \pi k,[/latex]  k∈Z [latex] \frac{x}{3} \neq \frac{ \pi }{2} + \pi n,[/latex] n∈Z [latex]x \neq \pi +2 \pi k,[/latex] k∈Z [latex]x \neq \frac{3 \pi }{2} +3 \pi n,[/latex] n∈Z [latex]sin( \frac{x}{2} + \frac{x}{3} )=0[/latex] [latex]sin \frac{5x}{6} =0[/latex] [latex] \frac{5x}{6} = \pi m,[/latex] m∈Z [latex]x= \frac{6 \pi m}{5} ,[/latex] m∈Z