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Q.
If $0 < \alpha < \frac{\pi }{3},$ then $\alpha \left(sec \alpha \right)$ is
NTA AbhyasNTA Abhyas 2020
Solution:
On the graph of $y=cos x$
Let $A\left(\alpha , cos \alpha \right)$ and $B\left(\frac{\pi }{3} , cos \frac{\pi }{3}\right)$
Clearly, slope of $OA>$ slope of $OB$
$\Rightarrow \frac{cos \alpha }{\alpha }>\frac{cos \frac{\pi }{3}}{\frac{\pi }{3}}$
$\Rightarrow \alpha sec \alpha < \frac{2 \pi }{3}$ .
