Question

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

• A. [ 0, 1]
• B. [ -1, 1]
• C. [1, 3]
• D. None of these

Answer 1

Answer: (C)

${\tan }^{-1}xand{\cot }^{-1}x$ exist for all $x\in R$
${\cos }^{-1}\left(2-x\right)$ exists if $-1\le 2-x\le 1$
i.e. $1\le x\le 31\le x\le 3$