- Let and , , and , then show that…

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

- Let

\theta \in \left(0, \frac{\pi}{4}\right)

and

t_1 = (\tan \theta)^{\tan \theta}

t_2 = (\tan \theta)^{\cot \theta}

t_3 = (\cot \theta)^{\tan \theta}

and

t_4 = (\cot \theta)^{\cot \theta}

, then show that

t_4 > t_3 > t_1 > t_2