Question

If $0<\alpha <\frac{\pi }{3},$ then $\alpha \left(sec\alpha \right)$ is

• A. less than $\frac{\pi }{3}$
• B. greater than $\frac{\pi }{3}$
• C. less than $\frac{2\pi }{3}$
• D. greater than $\frac{2\pi }{3}$

Answer 1

Answer: (C)

On the graph of $y=cosx$

Let $A\left(\alpha ,cos\alpha \right)$ and $B\left(\frac{\pi }{3},cos\frac{\pi }{3}\right)$
Clearly, slope of $OA>$ slope of $OB$
$\Rightarrow \frac{cos\alpha }{\alpha }>\frac{cos\frac{\pi }{3}}{\frac{\pi }{3}}$
$\Rightarrow \alpha sec\alpha <\frac{2\pi }{3}$ .