Statement I Number of roots of the equation is zero

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Statement I Number of roots of the equation

\cot^{-1} x \cos^{-1} 2x + \pi = 0

is zero. Statement II Range of

\cot^{-1} x

and

\cos^{-1} x

(0, \pi)

and

[0, \pi]

, respectively.