Solve, please. $$\displaystyle{\cos{{\left({2}{x}\right)}}}={1}$$

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autormtak0w
Isolate the variable by dividing each side by factors that don't contain the variable.
$$\displaystyle{x}=\pi{n}$$ for any integer n
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Toni Scott
$$\displaystyle{\cos{{\left({2}{x}\right)}}}={2}$$, $$\displaystyle{{\cos}^{{{2}}}{x}}-{1}={1}$$
$$\displaystyle{{\cos}^{{{2}}}=}{1}$$
$$\displaystyle{\cos{{\left({x}\right)}}}={1}$$, x=0 and $$\displaystyle{x}={2}\pi$$
$$\displaystyle{\cos{{\left({x}\right)}}}=-{1}$$, $$\displaystyle{x}=\pi$$
RizerMix

$$\cos(2x)=1$$
$$2x=2\pi k$$
$$x=\pi k$$
$$k\in Z$$