Question

$f\left(x\right)={\cos }^{2}x+{\sec }^{2}x\ge 2.$
or Min. value of $f\left(x\right)$ is $2$.

• A. True
• B. False

Answer 1

The correct option is A True

Ans. $True$.
$L.H.S.=(\cos x-\sec x{)}^2+2\cos x.\sec x$
$=2+(\cos x-\sec x{)}^2$
$\therefore f\left(x\right)\ge 2$
Similarly, min. value of ${\csc }^{2}x+{\sin }^{2}x$ and ${\cot }^{2}x+{\tan }^{2}x$ is also $2$.