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Prove that sin u/ sin v lies between u/v and pi/2 times u/v

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December 6, 2010

inequalitiestrigonometryfunctioncalculusinequalities unsolved

Problem Statement

Prove the inequalities

\frac{u}{v}\le \frac{\sin u}{\sin v}\le \frac{\pi}{2}\times\frac{u}{v},\text{ for }0 \le u < v \le \frac{\pi}{2}