Respuesta :

[tex]\bf 2[sin(x)]^2+\sqrt{3}sin(x)=2sin(x)+\sqrt{3} \\\\\\ 2[sin(x)]^2+\sqrt{3}sin(x)-2sin(x)-\sqrt{3}=0 \\\\\\\ [2sin^2(x)-2sin(x)]~+~[\sqrt{3}sin(x)-\sqrt{3}]=0 \\\\\\ \stackrel{common~factor}{2sin(x)}[sin(x)-1]~~+~~\stackrel{common~factor}{\sqrt{3}}[sin(x)-1]=0 \\\\\\[/tex]

[tex]\bf \stackrel{common~factor}{[sin(x)-1]}~[2sin(x)+\sqrt{3}]=0\qquad \begin{cases} sin(x)-1=0\\ sin(x)=1\\ \measuredangle x=\frac{\pi }{2}\\ ----------\\ 2sin(x)+\sqrt{3}=0\\ 2sin(x)=-\sqrt{3}\\ sin(x)=-\frac{\sqrt{3}}{2}\\\\ \measuredangle x=\frac{4\pi }{3}~,~\frac{5\pi }{3} \end{cases}[/tex]

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