Question

Подробно решение распишите пожалуйста
$4sin^{2} 3x textless 3$

Answer 1

$4sin^23x textless 3; ; Rightarrow ; ; 4sin^23x-3 textless 0\\(2sin3x-sqrt3)(2sin3x+sqrt3) textless 0\\t=sin3x; ,; ; ; (2t-sqrt3)(2t+sqrt3) textless 0\\Znaki:; ; ; +++(-frac{sqrt3}{2})---(frac{sqrt3}{2})+++; ; ; ; ; ; -frac{sqrt3}{2} textless t textless frac{sqrt3}{2}\\left { {{sin3x textless frac{sqrt3}{2}} atop {sin3x textgreater -frac{sqrt3}{2}}} right. ; left { {{-frac{4pi}{3}+2pi n textless 3x textless frac{pi}{3}+2pi n; ,; nin Z} atop {-frac{4pi }{3}+2pi k textless 3x textless -frac{pi}{3}+2pi k; ,; kin Z}} right. ; ; Rightarrow$

$left [ {{frac{2pi}{3}+2pi m textless 3x textless frac{4pi}{3}+2pi m; ,; min Z} atop {-frac{pi}{3}+2pi l textless 3x textless frac{pi}{3}+2pi l; ,; lin Z}} right. ; left [ {{frac{2pi}{9}+frac{2pi m}{3} textless x textless frac{4pi }{9}+frac{2pi m}{3}; ,; min Z} atop {-frac{pi}{9}+frac{2pi l}{3} textless x textless frac{pi}{9}+frac{2pi l}{3}}; ,lin Z} right.$