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Montrer que \[\forall x\in\R,\qquad |\sin x| \leq |x|,\] \[\forall x\in[0,\frac \pi 2], \qquad 1-\cos x \leq x \sin x,\] \[\forall x\in[-1,1],\qquad |\arcsin x| \leq \left| \frac x{\sqrt{1-x^2}} \right|.\]
Montrer que \[\forall x\in\R,\qquad |\sin x| \leq |x|,\] \[\forall x\in[0,\frac \pi 2], \qquad 1-\cos x \leq x \sin x,\] \[\forall x\in[-1,1],\qquad |\arcsin x| \leq \left| \frac x{\sqrt{1-x^2}} \right|.\]