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Let theta in (0,pi/4) and t1=(tan theta)...

Let `theta in (0,pi/4) and t_1=(tan theta)^(tan theta), t_2=(tan theta)^(cot theta), t_3=(cot theta)^(tan theta) and t_4=(cot theta)^(cot theta),` then

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As when `theta in (0, pi/4), tan theta< cot theta`
Since, `tan theta<1` and `cot theta>1`
(tan^theta)^(cot theta)<1` and `(cot^theta)^(tan theta)>1`
`t_4>t_1`
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