If 0 < α < (π)/(3), then α (sec α) is

0 < \alpha < \dfrac{\pi}{3}, then

\alpha

\left(sec \alpha\right)

Options

Aless than $\dfrac{\pi}{3}$
Bgreater than $\dfrac{\pi}{3}$
Cless than $\dfrac{2\pi}{3}$
Dgreater than $\dfrac{2\pi}{3}$

Correct answer

C. less than $\dfrac{2\pi}{3}$

Step-by-step solution

On the graph of $y = cos x$
If 0 < α < (π)/(3), then α (sec α) is
Let $ $A\left(\alpha, cos \alpha\right)$ and $B\left(\dfrac{\pi}{3}, cos \dfrac{\pi}{3}\right)$

Clearly, slope of $OA >$ slope of $OB$
$⇒ \dfrac{cos \alpha}{\alpha} > \dfrac{cos \dfrac{\pi}{3}}{\dfrac{\pi}{3}}$
$⇒ \alpha sec \alpha < \dfrac{2\pi}{3}.

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