Question

The range of $f\left(x\right)={\cos }^{2}x+{\sec }^{2}x$ is [a,$\infty$] Find a

Answer 1

We have $f\left(x\right)={\cos }^{2}x+{\sec }^{2}x$
$={(\cos x-\sec x)}^2+2\cos x\sec x$
$=2+{(\cos x-\sec x)}^2\ge 2$
Ans: 2