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MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

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: (1)

t_1>t_2>t_3>t_4

(2)

t_4>t_3>t_1>t_2

(3)

t_3>t_1>t_2>t_4

(4)

t_2>t_3>t_1>t_4