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min and max of tan(3x)/tan^3x in (0, \pi /2)

Source: Vietnamese MO (VMO) 1975 P5

August 20, 2018
algebrafunctionminimum valuemaximum valueanalysis

Problem Statement

Show that the sum of the (local) maximum and minimum values of the function tan(3x)tan3x\frac{tan(3x)}{tan^3x} on the interval (0,π2)\big(0, \frac{\pi }{2}\big) is rational.