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sin^3 a/ sin b +cos^3 a/cos b >= 2/cos(a - b)

Source: 2011 Saudi Arabia Pre-TST November 3.1

January 1, 2022
algebrainequalitiestrigonometry

Problem Statement

Prove that sin⁡3asin⁡b+cos⁡3acos⁡b≥1cos⁡(a−b)\frac{\sin^3 a}{\sin b} +\frac{\cos^3 a}{\cos b} \ge \frac{1}{\cos(a - b)} for all aa and bb in the interval (0,π/2)(0, \pi/2) .
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