Question

What is minimum value of ${\sec }^2\theta +{\cos }^2\theta$?

Answer 1

We know that
${(\sec \theta -\cos \theta )}^2\ge 0$
$\Rightarrow {\sec }^2\theta +{\cos }^2\theta -2\sec \theta \cos \theta \ge 0$
$\Rightarrow {\sec }^2\theta +{\cos }^2\theta -2\ge 0$
$\Rightarrow {\sec }^2\theta +{\cos }^2\theta \ge 0$
$\therefore$ least value of ${\sec }^2\theta +{\cos }^2\theta =2$