Let θ belong to (0,pi/4) and t 1 =(tanθ) tanθ ,t 2 =(tanθ) cot θ , t 3 =(cotθ) tanθ , t 4 = (cotθ) cotθ , then A)t 1 t 2 t 3 t 4 B) t 4 t 3 t 1 t 2 C) t 3 t 1 t 2 t 4 D)t 2 t 3 t 1 t 4

Question

Let θ belong to (0,pi/4) and t 1 =(tanθ) tanθ ,t 2 =(tanθ) cot θ , t 3 =(cotθ) tanθ , t 4 = (cotθ) cotθ , then ​A)t 1 >t 2 >t 3 >t 4 B) t 4 >t 3 >t 1 >t 2 C) t 3 >t 1 >t 2 >t 4 D)t 2 >t 3 >t 1 >t 4

Ravi · Answer

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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Let θ belong to (0,pi/4) and t 1 =(tanθ) tanθ ,t 2 =(tanθ) cot θ , t 3 =(cotθ) tanθ , t 4 = (cotθ) cotθ , then A)t 1 >t 2 >t 3 >t 4 B) t 4 >t 3 >t 1 >t 2 C) t 3 >t 1 >t 2 >t 4 D)t 2 >t 3 >t 1 >t 4

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

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Let θ belong to (0,pi/4) and t 1 =(tanθ) tanθ ,t 2 =(tanθ) cot θ , t 3 =(cotθ) tanθ , t 4 = (cotθ) cotθ , then ​A)t 1 >t 2 >t 3 >t 4 B) t 4 >t 3 >t 1 >t 2 C) t 3 >t 1 >t 2 >t 4 D)t 2 >t 3 >t 1 >t 4

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