Решите тригонометрическое уравнение:[latex](2cosx+1)( \sqrt{-sinx}-1)=0[/latex]

[latex](2\cos x+1)(\sqrt{-\sin x}-1)=0[/latex] [latex]\left\{\begin{array}{l} -\sin x \geq 0 \\ \left[\begin{array}{l} 2\cos x+1=0 \\ \sqrt{-\sin x}-1=0 \end{array} \end{array}[/latex] [latex]\left\{\begin{array}{l} \sin x \leq 0 \\ \left[\begin{array}{l} 2\cos x=-1 \\ \sqrt{-\sin x}=1 \end{array} \end{array}[/latex] [latex]\left\{\begin{array}{l} \sin x \leq 0 \\ \left[\begin{array}{l} \cos x=- \frac{1}{2} \\ \sin x=-1 \end{array} \end{array}[/latex] [latex]\left\{\begin{array}{l} \sin x \leq 0 \\ \left[\begin{array}{l} x=\pm \frac{2\pi}{3}+2\pi m \\ x=- \frac{ \pi }{2}+2\pi n \end{array} \end{array}[/latex] [latex]\left[\begin{array}{l} x=-\frac{2\pi}{3}+2\pi m, \ m\in Z \\ x=- \frac{ \pi }{2}+2\pi n, \ n\in Z \end{array} [/latex]