Question

The minimum value of $27{\tan }^2\theta +3{\cot }^2\theta$ is

• A. $15$
• B. $18$
• C. $24$
• D. $30$

Answer 1

The correct option is B $18$

As A.M. > G.M

$\frac{27{\tan }^2\theta +3{\cot }^2\theta }{2}\ge \sqrt{27{\tan }^2\theta 3{\cot }^2\theta }$

$27{\tan }^2\theta +3{\cot }^2\theta \ge 18$