Trigonometrical Ratios and Identities 3 Question 1
2. Let $\theta \in 0, \frac{\pi}{4}$ 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
(2006, 3M)
True/False
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Answer:
Correct Answer: 2. (b)
Solution:
- As when $\theta \in 0, \frac{\pi}{4}, \tan \theta<\cot \theta$
Since, $\quad \tan \theta<1$ and $\cot \theta>1$
$\therefore \quad(\tan \theta)^{\cot \theta}<1$ and $(\cot \theta)^{\tan \theta}>1$
$\therefore t _4>t _1$ which only holds in (b). Therefore, (b) is the answer.
