How do you solve #2cos^2x-cosx=1# and find all solutions in the interval #0<=x<360#?

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Answer 1 · 2016-09-27T18:32:02

#" The Soln. Set="{0,120,240} sub [0,360).#

#2cos^2x-cosx=1 rArr 2cos^2x-cosx-1=0#

#rArr 2cos^2x-2cosx+cosx-1=0#

#rArr 2cosx(cosx-1)+1(cosx-1)=0#

#rArr (cosx-1)(2cosx+1)=0#

#rArr cosx=1, cosx=-1/2#

#cosx=1, &, 0lexlt360 rArr x=0#

#cosx=-1/2, &, 0lexlt360 rArr x=180+-60=120, 240#

#:." The Soln. Set="{0,120,240} sub [0,360).#