# Find all values of x in the interval [0, 2pi] that satisfy the equation: 2cos x=- sin 2x

Find all values of x in the interval $\left[0,2\pi \right]$ that satisfy the equation:
$2\mathrm{cos}x=-\mathrm{sin}2x$
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Asdrubali2r
$2\mathrm{cos}x=-\mathrm{sin}2x$
$2\mathrm{cos}x=-2\mathrm{sin}x\mathrm{cos}x$
$\mathrm{cos}x-\mathrm{sin}x\mathrm{cos}x=0$
$\mathrm{cos}x\left(1+\mathrm{sin}x\right)=0$

Jeffrey Jordon