Question

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Answer 1

$2)Sin4x=Sin2x\\\\2Sin2xCos2x-Sin2x=0\\\\Sin2x(2Cos2x-1)=0\\\\\left[\begin{array}{ccc}Sin2x=0\\2Cos2x-1=0\end{array}\right\\\\\left[\begin{array}{ccc}Sin2x=0\\Cos2x=\frac{1}{2} \end{array}\right\\\\1)Sin2x=0\\\\2x=\pi n,n\in Z\\\\x=\frac{\pi n }{2},n\in Z$

$2)Cos2x=\frac{1}{2}\\\\2x=\pm arcCos\frac{1}{2}+2\pi n,n\in Z\\\\2x=\pm \frac{\pi }{3}+2\pi n,n\in Z\\\\x=\pm \frac{\pi }{6}+\pi n,n\in Z$

$4)Sin2x=Cos^{2}x\\\\2SinxCosx-Cos^{2}x=0\\\\Cosx(2Sinx-Cosx)=0\\\\\left[\begin{array}{ccc}Cosx=0\\2Sinx-Cosx=0\end{array}\right \\\\1)Cosx=0\\\\x=\frac{\pi }{2}+\pi n,n\in Z\\\\2)2Sinx-Cosx=0|:Sinx\neq 0\\\\2-Ctgx=0\\\\Ctgx=2\\\\x=arcCtg2+\pi n,n\in Z$