Question

If $f\left(\theta \right)=2({\sec }^2\theta +{\cos }^2\theta ),$ then its
value always

• A. $f\left(\theta \right)<2$
• B. $f\left(\theta \right)=2$
• C. $4>f\left(\theta \right)>2$
• D. $f\left(\theta \right)\ge 4$

Answer 1

The correct option is D $f\left(\theta \right)\ge 4$

$f\left(\theta \right)=2({\sec }^2\theta +{\cos }^2\theta )\Rightarrow f\left(\theta \right)=2(\sec \theta -\cos \theta {)}^2+4\sec \theta \cos \theta$
$\Rightarrow f\left(\theta \right)=2(\sec \theta -\cos \theta {)}^2+4\ge 4$