Question

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

• A. 15
• B. 18
• C. 24
• D. 30

Answer 1

Answer: (B)

Given trigonometrical equation is
$27{\tan }^2\theta +3{\cot }^2\theta$ (Using $AM\ge GM$)
$\therefore \frac{27{\tan }^2\theta +3{\cot }^2\theta }{2}\ge \sqrt{27{\tan }^2\theta \cdot 3{\cot }^2\theta }$
$\Rightarrow \frac{27{\tan }^2\theta +3{\cot }^2\theta }{2}\ge \sqrt{81}$
$\Rightarrow 27{\tan }^2\theta +3{\cot }^2\theta \ge 18$
Hence, minimum value of given equation is 18