Тригонометрическое неравенство: [latex]tg^2x-1\ \textgreater \ 0[/latex]

[latex]\mathrm{tg}^2x-1 \ \textgreater \ 0 \\\ (\mathrm{tg}x-1) (\mathrm{tg}x+1) \ \textgreater \ 0 [/latex] Замена: [latex]\mathrm{tg}x=a[/latex] [latex](a-1)(a+1)\ \textgreater \ 0 \\\ \Rightarrow \left [ {{a\ \textgreater \ 1} \atop {a\ \textless \ -1}} \right. [/latex] Возвращаемся к исходной переменной: [latex] \left [ {{\mathrm{tg}x\ \textgreater \ 1} \atop {\mathrm{tg}x\ \textless \ -1}} \right. \\\ \left [ {{x\in ( \frac{ \pi }{4}+ \pi n; \ \frac{ \pi }{2}+ \pi n) } \atop x\in ( \frac{ \pi }{2}+ \pi n; \ \frac{ 3\pi }{4}+ \pi n) }} \right. \\\ \Rightarrow x\in ( \frac{ \pi }{4}+ \pi n; \ \frac{ \pi }{2}+ \pi n) \cup ( \frac{ \pi }{2}+ \pi n; \ \frac{ 3\pi }{4}+ \pi n), \ n\in Z[/latex]