Inverse Trigonometric Functions Question 29
Question: The solution set of the equation $ {{\tan }^{-1}}x-{{\cot }^{-1}}x={{\cos }^{-1}}(2-x) $ will lie in the interval
Options:
A) $ [0,1] $
B) $ [-1,1] $
C) $ [1,3] $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ {{\tan }^{-1}}x $ and $ {{\cot }^{-1}}x $ exist for all $ x\in R $
$ {{\cos }^{-1}}(2-x) $ exists if $ -1\le 2-x\le 1 $ i.e. $ 1\le x\le 3 $
So, the given equation holds for $ 1\le x\le 3 $
BETA
