If 0 < α < (π)/(3), then α ( sec α)is

0 < \alpha < \dfrac{π}{3},

then

\alpha \left(

sec

\alpha\right)is

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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