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Let theta in (0, pi/4) and t(1)=tan thet...

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 show that `t_(4) gt t_(3) gt t_(1) gt t_(2)`.

A

`t_(1) gt t_(2) gt t_(3) gt t_(4)`

B

`t_(4) gt t_(3) gt t_(1) gt t_(2)`

C

`t_(3) gt t_(1) gt t_(2) gt t_(4)`

D

`t_(2) gt t_(3) gt t_(1) gt t_(4)`

Text Solution

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The correct Answer is:
B
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