[m]\left\{\begin{matrix} sinx \geq 0\\cosx\geq 0\\ sinx \geq \sqrt{3}cosx \end{matrix}\right.[/m]
⇒ [m]\left\{\begin{matrix} sinx \geq 0\\cosx\geq 0\\ tgx \geq \sqrt{3} \end{matrix}\right.[/m]
x ∈[ (π/3)+2πn;(π/2)+2πn], n ∈ Z
2.
[m]\left\{\begin{matrix} sinx \geq 0\\cosx< 0\\ sinx \geq -\sqrt{3}cosx \end{matrix}\right.[/m]
⇒ [m]\left\{\begin{matrix} sinx \geq 0\\cosx<0\\ tgx \leq -\sqrt{3} \end{matrix}\right.[/m]
x ∈[(π/2)+2πn;(2π/3)+2πn], n ∈ Z
3.
[m]\left\{\begin{matrix} sinx <0\\cosx< 0\\- sinx \geq -\sqrt{3}cosx \end{matrix}\right.[/m]
⇒ [m]\left\{\begin{matrix} sinx <0\\cosx< 0\\ tgx \geq \sqrt{3} \end{matrix}\right.[/m]
x ∈[ (-2π/3)+2πn;(-π/2)+2πn], n ∈ Z
4.
[m]\left\{\begin{matrix} sinx < 0\\cosx ≥ 0\\ -sinx \geq \sqrt{3}cosx \end{matrix}\right.[/m]
⇒ [m]\left\{\begin{matrix} sinx < 0\\cosx ≥ 0\\ tgx \leq -\sqrt{3} \end{matrix}\right.[/m]
x ∈( (-π/2)+2πn;(-π/3)+2πn], n ∈ Z
О т в е т. Объединение ответов 4-х рассмотренных случаев:
[ (π/3)+2πn;(π/2)+2πn]U[(π/2)+2πn;(2π/3)+2πn]U[ (-2π/3)+2πn;(-π/2)+2πn]U( (-π/2)+2πn;(-π/3)+2πn]=
=[ (π/3)+2πn;(2π/3)+2πn]U[ (-2π/3)+2πn;(-π/3)+2πn], n ∈ Z