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$2<\text{F}(\text{x})<1$
- D$\text{F}(\text{x})\geq2$
Solution:
$\text{f}(\text{x}) = \cos^2\text{x} + \sec^2\text{x}$
$=\cos^2\text{x} +\sec^2\text{x}-2\cos\text{x}\sec\text{x}+2\cos\text{x}\sec\text{x}$
$=(\sec\text{x}-\cos\text{x})^2 +2$
$\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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