First slide

Introduction to ITF

Question

The solution set of the equation $\tan^{- 1} x - \cot^{- 1} x =$ $\cos^{- 1} (2 - x)$ is

Moderate

A

[0, 1]
B

[– 1, 1]
C

[1, 3]
D

none of these

Solution

$\tan^{- 1} x and \cot^{- 1} x$ exist for all $x \in R$
$\cos^{- 1} (2 - x) exists if - 1 \leq 2 - x \leq 1 i.e. 1 \leq x \leq 3$
So, the given equation holds for $1 \leq x \leq 3$

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