How do you solve $cos(2(theta)) + 5 cos (theta) + 3$ ?

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Answer 1 · 2017-02-02T07:25:48

$theta=2npi+-(2pi)/3$

It appears that the questioner meant

$cos2theta+5costheta+3=0$

As this is equiavalent to $2cos^2theta-1+5costheta+3=0$

or $2cos^2theta+5costheta+2=0$

and using quadratic formula

$costheta=(-5+-sqrt(5^2-4xx2xx2))/4=(-5+-3)/4$

i.e $costheta=-2$ or $-1/2$

But as range of $costheta$ is $[-1,1]$ , we cannot have $costheta=-2$

Therefore $costheta=-1/2=cos((2pi)/3)$

Hence $theta=2npi+-(2pi)/3$

How do you solve cos(2(theta)) + 5 cos (theta) + 3cos(2(theta)) + 5 cos (theta) + 3?