Trigonometric Functions — MATHS STD 11 Science — Question

4. $\text{f(x)}\geq2$

Solution:

Given that; $\text{f(x)}=\cos^2\text{x}+\sec^2\text{x}$

We know that $\text{AM}\geq\text{GM}$

$\Rightarrow\frac{\cos^2\text{x}+\sec^2\text{x}}{2}\geq\sqrt{\cos^2\text{x}.\sec^2\text{x}}$

$\Rightarrow\frac{\cos^2\text{x}+\sec^2\text{x}}{2}\geq1$ $\big[\text{since}\sec\theta=\frac{1}{\cos\theta}\big]$

$\Rightarrow\cos^2\text{x}+\sec^2\text{x}\geq2$

$\Rightarrow\text{f(x)}\geq2$

Hence, the correct option is (d)