MCQ
The minimum value of $9{\tan ^2}\theta + 4{\cot ^2}\theta $ is
  • A
    $13$
  • B
    $9$
  • C
    $6$
  • $12$

Answer

Correct option: D.
$12$
d
(d) $A.M.\,\,  \ge \,\, G.M. $

$ \Rightarrow \frac{{9{{\tan }^2}\theta + 4{{\cot }^2}\theta }}{2} \ge \sqrt {4{{\cot }^2}\theta .9{{\tan }^2}\theta } $ 

$ \Rightarrow 9{\tan ^2}\theta + 4{\cot ^2}\theta \ge 12$ 

Therefore, the minimum value is $12.$

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