\(sin2x+sin^2x=\dfrac{1}{2}\)
\(\Leftrightarrow sin2x+\dfrac{1}{2}\left(2sin^2x-1\right)=0\)
\(\Leftrightarrow sin2x-\dfrac{1}{2}cos2x=0\)
\(\Leftrightarrow\dfrac{\sqrt{5}}{2}\left(\dfrac{2}{\sqrt{5}}sin2x-\dfrac{1}{\sqrt{5}}cos2x\right)=0\)
\(\Leftrightarrow\dfrac{\sqrt{5}}{2}sin\left(2x-arccos\dfrac{2}{\sqrt{5}}\right)=0\)
\(\Leftrightarrow2x-arccos\dfrac{2}{\sqrt{5}}=k\pi\)
\(\Leftrightarrow x=\dfrac{1}{2}arccos\dfrac{2}{\sqrt{5}}+\dfrac{k\pi}{2}\)
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