Tgx=ctgx подскажите как решить

[latex]tg(x)=ctg(x)[/latex] [latex]tg(x)= \frac{1}{tg(x)} [/latex] [latex]tg(x)- \frac{1}{tg(x)} =0[/latex] [latex] \frac{tg^2(x)-1}{tg(x)}=0 [/latex] [latex] \frac{(tg(x)-1)(tg(x)+1)}{tg(x)}=0 [/latex] [latex] \left \{ {{tg(x)=\pm1} \atop {tg(x) \neq 0}} \right. ; \left \{ {{x= \pm\frac{\pi}{4}+\pi n,n\in Z} \atop {x \neq \pi n, n \in Z}} \right. ;x= \pm\frac{\pi}{4}+\pi n,n\in Z[/latex] Ответ: [latex]\pm\frac{\pi}{4}+\pi n,n\in Z[/latex]