First slide

Properties of ITF

Question

The least integral value of $x$ for which $\tan^{- 1} x > \cot^{- 1} x$ is

Easy

A

1
B

2
C

3
D

4

Solution

$W e h a v e \tan^{- 1} x > c o t^{- 1} x \Rightarrow \tan^{- 1} x > \frac{π}{2} - \tan^{- 1} x \Rightarrow 2 \tan^{- 1} x > \frac{π}{2} \Rightarrow \tan^{- 1} x > \frac{π}{4} \Rightarrow x > \tan \frac{π}{4} \Rightarrow x > 1 ∴ t h e l e a s t i n t e g r a l v a l u e o f x i s 2$

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