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Let $\theta \in\left(0, \frac{\pi}{4}\right)$ and $t_1=(\tan \theta)^{\tan \theta}, t_2=(\tan \theta)^{\cot \theta}$ and $t_4=(\cot \theta)^{\tan \theta}$, then
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The correct answer is:
$t_4>t_3>t_1>t_2$
$t_4>t_3>t_1>t_2$
As when $\theta \in\left(0, \frac{\pi}{4}\right)$
$\tan \theta < \cot \theta$
Since, $\tan \theta < 1$ and $\cot \theta>1$
$\therefore(\tan \theta)^{\cot \theta} < 1$ and $(\cot \theta)^{\tan \theta}>1$
$\therefore t_4>t_1$ which only holds in option (b).
$\tan \theta < \cot \theta$
Since, $\tan \theta < 1$ and $\cot \theta>1$
$\therefore(\tan \theta)^{\cot \theta} < 1$ and $(\cot \theta)^{\tan \theta}>1$
$\therefore t_4>t_1$ which only holds in option (b).
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