Question

The minimum value of
$9{\tan }^2\theta +4{\cot }^2\theta$ is

• A. $13$
• B. $9$
• C. $12$
• D. $6$

Answer 1

The correct option is C

$12$

$9{\tan }^2\theta +4{\cot }^2\theta =9{\tan }^2\theta +4{\cot }^2\theta -12+12=(3\tan \theta -2\cot \theta {)}^2+12$
So the minimum value of$=12$