If F(x)= ^2x+ ^2x, then - Vidyadip

MCQ

If $\text{F}(\text{x})=\cos^2\text{x}+\sec^2\text{x},$ then

A
$\text{F}(\text{x})<1$
B
$\text{F}(\text{x})=1$
C
$2<\text{F}(\text{x})<1$
✓
$\text{F}(\text{x})\geq2$

✓

Answer

Correct option: D.

$\text{F}(\text{x})\geq2$

$\text{f}(\text{x}) = \cos^2\text{x} + \sec^2\text{x}$
$=\cos^2\text{x} +\sec^2\text{x}-2\cos\text{x}\sec\text{x}+2\cos\text{x}\sec\text{x}$
$=(\sec\text{x}-\cos\text{x})^2 +2$
$\therefore\text{f}\text({x})\geq 2 \ \forall \text{ x }$$\Big[(\sec\text{x}-\cos\text{x})^2\geq 0 \ \forall \text{ x}\Big]$
Hence, the correct option is answer $D.$

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