Trigonometric EquationHard
Question
Let θ ∈ 
and t1 = (tan θ)tan θ, t2 = (tan θ)cot θ, t3 = (cot θ)tan θ and t4 = (cotθ)cot θ, then
and t1 = (tan θ)tan θ, t2 = (tan θ)cot θ, t3 = (cot θ)tan θ and t4 = (cotθ)cot θ, thenOptions
A.t1 > t2 > t3 > t4
B.t4 > t3 > t1 > t2
C.t3 > t1 > t2 > t4
D.t2 > t3 > t1 > t4
Solution
Given θ ∈ , then tan θ < 1 and cotθ > 1.
Let tan θ = 1 - λ1 and cot θ = 1 + λ2 where λ1 and λ2 are very small and positive.
then t1 = (1 - λ1)1-λ1, t2 = ( - λ1)1+λ2
t3 = (1 + λ2)1-λ1 and t4 = (1 + λ2)1+λ2
Hence t4 > t3 > t1 > t2.
, then tan θ < 1 and cotθ > 1.Let tan θ = 1 - λ1 and cot θ = 1 + λ2 where λ1 and λ2 are very small and positive.
then t1 = (1 - λ1)1-λ1, t2 = ( - λ1)1+λ2
t3 = (1 + λ2)1-λ1 and t4 = (1 + λ2)1+λ2
Hence t4 > t3 > t1 > t2.
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