The minimum value of 9 ^2 + 4 ^2 is - Vidyadip

Question

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

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Answer

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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