How do you solve $2cos^2 theta = cos theta$ if $(0 < theta < 2pi)$ ?

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Answer 1 · 2016-01-22T17:19:51

$2cos^2theta=costheta$

$implies 2cos^2theta-costheta=0$

$implies costheta(2costheta-1)=0$

$implies Costheta=0 or 2costheta-1=0$
$implies theta=cos^-1(0) or theta=cos^-1(1/2)$

$implies theta=pi/2, (3pi)/2 or theta=pi/3, (5pi)/3$

$implies theta=pi/2, (3pi)/2, pi/3, (5pi)/3$

$implies theta=pi/3 pi/2, (3pi)/2, (5pi)/3$

How do you solve 2cos^2 theta = cos theta2cos^2 theta = cos theta if (0 < theta < 2pi)(0 < theta < 2pi)?