Question

The minimum value of ${\sec }^2\theta +cose{c}^2\theta$ is

• A. 2
• B. 4
• C. 0
• D. 1

Answer 1

Answer: (B)

${\sec }^2\theta +cose{c}^2\theta =1+{\tan }^2\theta +1+{\cot }^2\theta$
$=2+{\left(\tan \theta -\cot \theta \right)}^2+2\tan \theta \cot \theta$
$=2+2+{\left(\tan \theta -\cot \theta \right)}^2\ge 4.$