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.