Question 544641
Find the exact solutions in the interval [ 0 , 2π] for cos 2x – cos x = 0
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cos2x – cosx = 0
Identity: cos 2x=2cos^2x-1
2cos^2x-1 – cosx = 0
2cos^2x– cosx-1  = 0
(2cosx+1)(cosx-1)=0
..
2cosx+1=0
cosx=-1/2
x=2&#960;/3 and 4&#960;/3 (in quadrants II and III where cos<0
..
cosx-1=0
cosx=1
x=0
..
ans: 
Exact solutions in the interval [ 0 , 2&#960;]
x=0, 2&#960;/3 and 4&#960;/3