Inverse Trigonometric Functions Question 35
Question: If $ [si{n^{-1}}co{s^{-1}}si{n^{-1}}ta{n^{-1}}x]=1, $ where $ [.] $ denotes the greatest integer function, then x belongs to the interval
Options:
A) $ [tansincos1,tansincossin1] $
B) $ (tansincos1,tansincossin1) $
C) $ [-1,1] $
D) $ [sincostan1,sincostan1] $
Show Answer
Answer:
Correct Answer: A
We have, $ 1\le {{\sin }^{-1}}{{\cos }^{-1}}{{\sin }^{-1}}{{\tan }^{-1}}x\le \frac{\pi }{2} $
$ \Rightarrow \sin 1\le {{\cos }^{-1}}{{\sin }^{-1}}{{\tan }^{-1}}x\le 1 $
$ \Rightarrow \cos \sin 1\ge {{\sin }^{-1}}{{\tan }^{-1}}x\ge \cos 1 $
$ \Rightarrow \sin \cos \sin 1\ge {{\tan }^{-1}}x\ge \sin \cos 1 $
$ \Rightarrow \tan \sin \cos \sin 1\ge x\ge \tan sincos1 $
$ \therefore x\in [tansincos1,tansincossin1] $
BETA
