Question

2sin(2x)-sqrt{3}=0

Answer 1

\[2\sin(2x)-\sqrt{3}=0\]


\[2\sin(2x)=\sqrt{3}\]


\[\sin(2x)=\frac{\sqrt{3}}{2}\]


\[2x=\frac{\pi}{3} \ \textrm{or} \ 2x=\frac{2\pi}{3}\]


\[2x=\frac{\pi}{3} +2\pi n \ \textrm{or} \ 2x=\frac{2\pi}{3}+2\pi n\]


\[x=\frac{\pi}{6} +\pi n \ \textrm{or} \ x=\frac{2\pi}{6}+\pi n\]


\[x=\frac{\pi}{6} +\pi n \ \textrm{or} \ x=\frac{\pi}{3}+\pi n\]


So the solutions are


\[x=\frac{\pi}{6} +\pi n \ \textrm{or} \ x=\frac{\pi}{3}+\pi n\]


where n is an integer.