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\(sin2x=1\Rightarrow2x=\frac{\pi}{2}+k2\pi\Rightarrow x=\frac{\pi}{4}+k\pi\)
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\(\frac{1}{2}sin2x=0\Rightarrow sin2x=0\Rightarrow2x=k\pi\Rightarrow x=\frac{k\pi}{2}\)
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\(sin^4x=cos^4x\Rightarrow\left[{}\begin{matrix}sinx=cosx\\sinx=-cosx\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+k\pi\\x=-\frac{\pi}{4}+k\pi\end{matrix}\right.\)
\(\Rightarrow x=\frac{\pi}{4}+\frac{k\pi}{2}\)
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\(2cos2x=-2\Rightarrow cos2x=-1\Rightarrow2x=\pi+k2\pi\)
\(\Rightarrow x=\frac{\pi}{2}+k\pi\)
\(\Leftrightarrow sin2x=1\Rightarrow2x=\frac{\pi}{2}+k2\pi\Rightarrow x=\frac{\pi}{4}+k\pi\)