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#