Let θ belong to (0,pi/4) and t₁ =(tanθ)^tanθ,t₂=(tanθ)^{cot θ}, t₃=(cotθ)^tanθ, t₄= (cotθ)^cotθ, then

​A)t₁>t₂>t₃>t₄ B) t₄>t₃>t₁>t₂ C) t₃>t₁>t₂>t₄ D)t₂>t₃>t₁>t₄

B

In the given interval, observe the graph and the maximum and minimum values the graphs of cotθ andtanθ attain. For the given interval,tanθ increases from 0 till 1. So most of the values would be less than 1 and greather than 0. For cotθ, it would decrease from infinity to 1. Hence, cotθ will always be greater than 1 in the given interval. numbers less than 1 when raised to large power tend to diminish more. Cotθ is a big number andtanθ is very small number in comparison. Use the analogy and put the values to understand the answer.

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