Inverse Trigonometric Functions Question 41
Question: Complete solution set of $ {{\tan }^{2}}(si{n^{-1}}x)>1 $ is
Options:
A) $ ( -1,-\frac{1}{\sqrt{2}} )\cup ( \frac{1}{\sqrt{2}},1 ) $
B) $ ( -\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} )\tilde{\ }{0} $
C) $ (-1,1)\tilde{\ }{0} $
D) None of these
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Answer:
Correct Answer: 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 ( \frac{1}{\sqrt{2}},1 )orx\in ( -1,-\frac{1}{\sqrt{2}} ) $
$ \Rightarrow x\in ( -1,-\frac{1}{\sqrt{2}} )\cup ( \frac{1}{\sqrt{2}},1 ) $
BETA
