First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $f (x) = \cos^{2} x + \sec^{2} x$ then

Easy

A

$f (x) < 1$
B

$f (x) = 1$
C

$2 < f (x) < 1$
D

$f (x) \geq 2$

Solution

$A M \geq G M$
$\Rightarrow \frac{\cos^{2} x + \sec^{2} x}{x} \geq \sqrt{\cos^{2} x . \sec^{2} x}$
$\Rightarrow \cos^{2} x + \sec^{2} x \geq 2$

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