[tex]\bf 4sin^2(x)-1=0\qquad [0,2\pi )
\\\\\\
4sin^2(x)=1\implies sin^2(x)=\cfrac{1}{4}\implies sin(x)=\pm\sqrt{\cfrac{1}{4}}
\\\\\\
sin(x)=\pm\cfrac{\sqrt{1}}{\sqrt{4}}\implies sin(x)=\pm\cfrac{1}{2}
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\measuredangle x= sin^{-1}\left( \pm\cfrac{1}{2} \right)\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}\\\\
\frac{5\pi }{6}\\\\
\frac{7\pi }{6}\\\\
\frac{11\pi }{6}
\end{cases}[/tex]
