Question

If $f\left(x\right)=co{s}^{2}x+se{c}^{2}x$, then

• A. $f(x)<1$
• B. $f(x)=1$
• C. $2<f(x)<1$
• D. $f(x)\ge 2$

Answer 1

Answer: (D)

Given, $f(x)=co{s}^{2}x+se{c}^{2}x$
Using $A.M.\ge G.M.$
$\therefore \frac{co{s}^{2}x+se{c}^{2}x}{2}\ge \sqrt{co{s}^{2}x\times se{c}^{2}x}$
$\Rightarrow co{s}^{2}x+se{c}^{2}x\ge 2$
$\therefore f\left(x\right)\ge 2$