Question

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

Answer 1

Let $y=9{\tan }^2\theta +4{\cot }^2\theta =(3\tan \theta -2\cot \theta {)}^2+12$
Hence minimum value of $y$ is $12\Rightarrow k=6$