How to find all solutions to the following equations, writing your answers in radians using exact values only?

Question

Find all solutions to the following equations. Write your answers in radians using
exact values only:
cos 2x − 3 cos x = −2

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Answer 1 · 2018-05-15T23:52:02

#cos2x− 3 cos x = −2#

#=>2cos^2x-1− 3 cos x +2=0#

#=>2cos^2x− 3 cos x +1=0#

#=>2cos^2x− 2 cos x -cosx+1=0#

#=>2cosx(cosx-1) -1(cosx-1)=0#

#=>(cosx-1)(2cosx -1)=0#

When #cosx=1#

#=>x=2npi" where "n inZZ#

When #2cosx -1=0#

#=>cosx=1/2=cos(pi/3)#

#=>x=2kpipmpi/3" where "k in ZZ#