[JEE Advanced 2006] for theta in 0 pi 4 let t 1 tan theta tan theta t
For $\theta\in(0,\frac\pi4)$, let $t_1=(\tan\theta)^{\tan\theta},\ t_2=(\tan\theta)^{\cot\theta},\ t_3=(\cot\theta)^{\tan\theta},\ t_4=(\cot\theta)^{\cot\theta}$. Then
(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) $t_2>t_3>t_1>t_4$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (b) $t_4>t_3>t_1>t_2$
On $(0,\frac\pi4)$, $\tan\theta<1<\cot\theta$. Comparing exponents/bases gives $t_4>t_3>t_1>t_2$.
JEE Advanced 2006 · Trigonometry — verified solution by the Vidaara Team.
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