Как решить 5tgx-4ctgx+8=0

[latex]5tgx-4ctgx+8=0 [/latex] [latex]5tgx- \frac{4}{tgx} +8=0[/latex] [latex]5 tgx^{2} +8tgx-4=0[/latex] [latex]D= \sqrt{64+4*5*4=144} , \sqrt{144} =12[/latex] [latex]tgx1= \frac{-8+12}{10} = \frac{2}{5} [/latex] [latex]tgx2= \frac{-8-12}{10} =-2[/latex] [latex]x1=arctg \frac{2}{5} + \pi n[/latex] [latex]x2=-arctg2+ \pi n[/latex]