Решите уравнения:tgx-4ctgx=3

[latex]tgx-4ctgx=3, \quad ctgx=\frac{1}{tgx}, \quad tgx*ctgx=1;\\tgx-\frac{4}{tgx}-3=0|*tgx\\tg^2x-3tgx-4=0, \quad tgx=u\\u^2-3u-4=0\\D:9+16=25\\u_1,_2=\frac{3\pm 5}{2}, \quad u_1=4, \; \; u_2=-1;\\\\tgx_1=4\\x_1=arctg4+\pi n, \; n\in Z;\\\\tgx_2=-1\\x_2=-\frac{\pi}{4}+\pi n, \; n\in Z.[/latex]