Exercise 14, § 1

Functions of a Real Variable, III, 118

Let $a$ be a real number such that $0 < a < \pi/2$ . Show that the function

\frac{\tan x}{x} - \frac{\tan a}{a}

is strictly increasing on the interval

]a, \pi/2[

(cf. I, p. 39, exerc. 11).

Solution

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