First slide

Extreme values and Periodicity of Trigonometric functions

Question

$f (x) = 2 + \cos^{2} x + \sec^{2} x its value always$

Easy

A

$f (x) < 1$
B

$f (x) = 1$
C

$27 f (x) > 1$
D

$f (x) \geq 4$

Solution

We have
$\begin{array}{l} \frac{\cos^{2} x + \sec^{2} x}{2} \geq \sqrt{\cos^{2} x \sec^{2} x} (∵ A M \geq G M) \\ \Rightarrow \cos^{2} x + \sec^{2} x \geq 2 \\ ∴ f (x) \geq 4 \end{array}$

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