• # question_answer The minimum value of $3{{\tan }^{2}}\theta +12{{\cot }^{2}}\theta$ is A) 6 B) 15 C) 24         D) none of these

Using $A.M.\ge G.M$ $\Rightarrow$$\frac{1}{2}(3{{\tan }^{2}}\theta +12{{\cot }^{2}}\theta )\ge 6$ $\Rightarrow$$3{{\tan }^{2}}\theta +12{{\cot }^{2}}\theta$has minimum value 12.