A) \[\left( -1,-\frac{1}{\sqrt{2}} \right)\cup \left( \frac{1}{\sqrt{2}},1 \right)\]
B) \[\left( -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)\tilde{\ }\{0\}\]
C) \[(-1,1)\tilde{\ }\{0\}\]
D) None of these
Correct Answer: A
Solution :
[a] \[{{\tan }^{2}}(si{{n}^{-1}}x)>1\] \[\Rightarrow \frac{\pi }{4}<{{\sin }^{-1}}x<\frac{\pi }{2}\] or \[-\frac{\pi }{2}<{{\sin }^{-1}}x<-\frac{\pi }{4}\] \[\Rightarrow x\in \left( \frac{1}{\sqrt{2}},1 \right)orx\in \left( -1,-\frac{1}{\sqrt{2}} \right)\] \[\Rightarrow x\in \left( -1,-\frac{1}{\sqrt{2}} \right)\cup \left( \frac{1}{\sqrt{2}},1 \right)\]
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