Question

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

• A. $x\in (0,1)$
• B. $x\in (-1,1)$
• C. $x\in (-\infty ,-1)$
• D. $x\in (1,\infty )$

Answer 1

The correct option is D $x\in (1,\infty )$

${\tan }^{-1}x>{\cot }^{-1}x\Rightarrow 2{\tan }^{-1}x>\frac{\pi }{2}(\because {\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2})\Rightarrow {\tan }^{-1}x>\frac{\pi }{4}\therefore x\in (1,\infty )$