Question

The minimum value of $3{\tan }^2\theta +12{\cot }^2\theta is$

• A. 6
• B. 15
• C. 24
• D. None of these

Answer 1

Answer: (D)

None of these

given $3ta{n}^2\theta +12co{t}^2\theta$

for a,b AM $\ge$ GM

$\frac{a+b}{2}\ge \sqrt{ab}$

$a+b\ge \sqrt{ab}$

$3ta{n}^2\theta +12co{t}^2\theta \ge 2\sqrt{3ta{n}^2\theta \times 12co{t}^2\theta }$

$\ge 2\sqrt{36(tan\theta cot\theta {)}^2}$

$\ge 2\sqrt{36}$

$\ge 2.6\ge 12$

$\therefore$ minimum volume =12