Question: Show that |eix - 1| |x| for all x ( R). Write eix = cosx + i sin x, express cosx in terms of

Show that |eix - 1| ≤ |x| for all x ( R).
Write eix = cosx + i sin x, express cosx in terms of sin2 x/2, and use the inequality | sin t | ≤ |t|, t ( R (which you also must prove).

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