A) \[[tan\,sin\,cos1,tan\,sin\,cos\,sin1]\]
B) \[(tan\,sin\,cos1,tan\,sin\,cos\,sin1)\]
C) \[[-1,1]\]
D) \[[sin\,cos\,tan1,sin\,cos\,tan1]\]
Correct Answer: A
Solution :
[a] We have, \[1\le {{\sin }^{-1}}{{\cos }^{-1}}{{\sin }^{-1}}{{\tan }^{-1}}x\le \frac{\pi }{2}\] \[\Rightarrow \sin 1\le {{\cos }^{-1}}{{\sin }^{-1}}{{\tan }^{-1}}x\le 1\] \[\Rightarrow \cos \sin 1\ge {{\sin }^{-1}}{{\tan }^{-1}}x\ge \cos 1\] \[\Rightarrow \sin \cos \sin 1\ge {{\tan }^{-1}}x\ge \sin \cos 1\] \[\Rightarrow \tan \sin \cos \sin 1\ge x\ge \tan \,sin\,cos1\] \[\therefore x\in [tan\,sin\,cos1,tan\,sin\,cos\,sin1]\]
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