How do you solve $Cos 2 theta = cos theta$ ?

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Answer 1 · 2016-05-23T08:56:54

$theta=(2n+1)pi/2$ or $theta=2npi+-(2pi)/3$ , where $n$ is an integer.

$cos2theta=costheta$

or $2cos^2theta-1=costheta$ (using formula for $cos2theta$ )

the above becomes $2cos^2theta-costheta-1=0$

Now using quadratic formula

$costheta=(-(-1)+-sqrt((-1)^2-4*2*(-1)))/(2*2)$

or $costheta=(1+-sqrt(1+8))/4=(1+-3)/4$

Hence $costheta=1=cos0$ or $costheta=-1/2=cos((2pi)/3)$

Hence $theta=(2n+1)pi/2$ or $theta=2npi+-(2pi)/3$ , where $n$ is an integer.

How do you solve Cos 2 theta = cos thetaCos 2 theta = cos theta?