﻿ Given θ Ïµ (0,π/4) and t1 = (tan θ)tanθ t2 = (tan θ)cotθ, t3 = (cot θ)tanθand t4 = (cot θ)cotθ then : Kaysons Education

# Given θ Ïµ (0,π/4) And t1 = (tan θ)tanθ t2 = (tan θ)cotθ, t3 = (cot θ)tanθand t4 = (cot θ)cotθ then

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## Question

### Solution

Correct option is

t4 > t3 > t1 > t2

θ Ïµ (0,π/4)

0 < tan θ < 1 and cos θ > 1 ⇒ log cot θ > 0

Now t1 = (tan θ)tanθ ⇒ log t1 = tan θ log (tan θ

Similarly log t2 = – cot θ log (cot θ

log t3 = tan θ log (cot θ), log t4 = cot θ log (cot θ)
As cot θ > tan θ, we have

log t4 > log t3 > log t1 > log t2

⇒ t4 > t3 > t1 > t2

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