Q. The solution set of the equation $\tan^{- 1}{x - \cot^{- 1}{x = \cos^{- 1}{(2 - x)is}}}$
A) [0,1]
B) $\lbrack - 1,1\rbrack$
C) [1,3]
D) None of these
Explanation
(c)
Since, $\tan^{- 1}{x\ and\cot^{- 1}x}$ exists for all $x \in \$R and $\cos^{- 1}{(2 - x)\ exists,\ \ }$ if $- 1 \leq 2 - x \leq 1$
$\therefore\tan^{- 1}{x - \cot^{- 1}{x = \cos^{- 1}{(2 - x)}}}$
Is possible only if 1$\leq x \leq 3.$
Thus the solution of given equation is [1, 3].
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.