# What is the solution of cos2x - cos x = 0 text{in the interval} [0, 2pi ) ?

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Let use the trigoniometric identity $\mathrm{cos}2x=2{\mathrm{cos}}^{2}x-1:$
$2{\mathrm{cos}}^{2}x-1-\mathrm{cos}x=0$
Factorize: $\left(\mathrm{cos}x-1\right)\left(2\mathrm{cos}x+1\right)=0$
Use the zero product property:
Solve both equations to consine:
$\mathrm{cos}x=1$ when $x=0$
$x=-\frac{1}{2}$ when
Aswer: $x=0,\left(\frac{2\pi }{3}\right),\left(4\pi \right)/3$