Find all solutions of the equation in the interval [0, 2π]. 5 cos^3 x = 5 cos x
5cos3x = 5cosxFirstly -5cosx from both sides and divide through by 5We have:cos3x-cosx = 0We can factorise this:cosx(cos2x - 1) = 0 For this to be true either:cosx = 0 or cos2x = 1for cosx = 0This occurs at pi/2 and 3pi/2.for cos2x = 1We have cosx = +/- 1 (do not forget to take +/- sqrt)This occurs at 0, pi, 2pi.Our solutions are:x = 0, pi/2, pi, 3pi/2, 2pi
GC
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