Question 1152146
One way is to graph cos(x) and cos(3x) on [0,2pi) and see where the graphs have the same y-value:<br>

*[illustration cos(x)_cos(3x)] 

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Another way is to graph cos(x) - cos(3x) and look for points where this difference function crosses, or touches, the x-axis:


 *[illustration diff]


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From the difference function, we see 0, pi/2, pi, and 3pi/2 are solutions.

Check:
cos(0) = cos(3*0) = 1
cos(pi/2) = cos(3pi/2) = 0
cos(pi) = cos(3pi) = -1
cos(3pi/2) = cos(9pi/2) = 0