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Let $θ \in (0, \frac{π}{4})$ and $t_{1} = {(\tan θ)}^{\tan θ}$ , $t_{2} = {(\tan θ)}^{c o t θ}$ , $t_{3} = {(c o t θ)}^{\tan θ}$ and $t_{4} = {(c o t θ)}^{c o t θ}$ then

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$t_{4} > t_{3} > t_{1} > t_{2}$

$t_{3} > t_{1} > t_{2} > t_{4}$

$t_{1} > t_{2} > t_{3} > t_{4}$

$t_{2} > t_{3} > t_{1} > t_{4}$

answer is B.

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Detailed Solution

$\begin{array}{l} In (0, \frac{π}{4}), \tan θ < 1 and \cot θ > 1 \\ \Rightarrow (\cot θ)^{\cot θ} > (\cot θ)^{\tan θ} > (\tan θ)^{\tan θ} > (\tan θ)^{\cot θ} \\ \Rightarrow∴ t_{4} > t_{3} > t_{1} > t_{2} \end{array}$

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