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JEE Advanced 2006

Exam: JEE Advanced
Year: 2006
Subject: Mathematics
Chapter: Trigonometric Ratios & Identities

JEE Advanced 2006 · Mathematics · Trigonometric Ratios & Identities

Let θ ∈ (0, (π)/(4)) and t_1=( θ)^ θ , t_2=( θ)^ θ and t_4=( θ)^ θ...

Let

\theta \in

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

and

t_1=(\tan \theta)^{\tan \theta}, t_2=(\tan \theta)^{\cot \theta} and

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

, then

Options

A $t_1>t_2>t_3>t_4$
B $t_4>t_3>t_1>t_2$
C $t_3>t_1>t_2>t_4$
D $t_2>t_3>t_1>t_4$

Correct answer

B. $t_4>t_3>t_1>t_2$

Step-by-step solution

As when

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

\tan \theta < \cot \theta

Since,

\tan \theta < 1

and

\cot \theta>1 \therefore(\tan \theta)^{\cot \theta} < 1

and

(\cot \theta)^{\tan \theta}>1 \therefore t_4>t_1$ which only holds in option (b).

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