Three Differences, Ordered

Problem

For 0<a<b<π20 < a < b < \dfrac{\pi}{2}, arrange in increasing order:

b−a,sin⁡b−sin⁡a,tan⁡b−tan⁡a.b - a, \qquad \sin b - \sin a, \qquad \tan b - \tan a.

Answer

Solution

Difficulty6/10
Topicstrigonometry, Mean Value Theorem, calculus

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