Ibrahim Rosales

2022-07-25

Solve the equation on the interval $\left[0,2\pi \right]$
$\mathrm{cos}2x=\sqrt{2}-\mathrm{cos}2x$

abortargy

Expert

$\mathrm{cos}2x=\sqrt{2}-\mathrm{cos}2x$
$⇒2\mathrm{cos}2x=\sqrt{2}$
$⇒\mathrm{cos}2x=\frac{\sqrt{2}}{2}$
$⇒\mathrm{cos}2x=\frac{1}{\sqrt{2}}$
$⇒2x={\mathrm{cos}}^{-1}\left(\frac{1}{\sqrt{2}}\right)$

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