Question

Let $\theta \in (0,\frac{\pi}{4})$ and t₁ = $(tan{\theta})^{tan{\theta}}$, t₂ = $(tan{\theta})^{cot{\theta}}$, t₃ = $(cot{\theta})^{tan{\theta}}$ and t₄ = $(cot{\theta})^{cot{\theta}}$, then
(a) t₁ > t₂ > t₃ > t₄
(b) t₄ > t₃ > t₁ > t₂
(c) t₃ > t₁ > t₂ > t₄
(d) t₂ > t₃ > t₁ > t₄

Answer 1

I think c is correct answers

But you can ask your teacher also

Answer 2

Answer:

(c) t₃ > t₁ > t₂ > t₄

Step-by-step explanation:

Let $\theta \in (0,\frac{\pi}{4})$ and t₁ = $(tan{\theta})^{tan{\theta}}$, t₂ = $(tan{\theta})^{cot{\theta}}$, t₃ = $(cot{\theta})^{tan{\theta}}$ and t₄ = $(cot{\theta})^{cot{\theta}}$, then

(a) t₁ > t₂ > t₃ > t₄

(b) t₄ > t₃ > t₁ > t₂

(c) t₃ > t₁ > t₂ > t₄

(d) t₂ > t₃ > t₁ > t₄