Trigonometric Identities Question 286
Question: Domain of the function $ f(x)=\sqrt{\frac{1}{\sin x}-1}, $ is
Options:
A) $ \underset{n\in I}{\mathop{\bigcup }},( 2n\pi ,2n\pi +\frac{\pi }{2} ) $
B) $ \underset{n\in I}{\mathop{\bigcup }},[2n\pi ,,(2n+1)\pi ] $
C) $ \underset{n\in I}{\mathop{\bigcup }},[(2n-1)\pi ,2n\pi ] $
D) None of these
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Answer:
Correct Answer: B
Solution:
$ \frac{1}{\sin x}-1\ge 0; $ $ \frac{1-\sin x}{\sin x}\ge 0 $ $ \frac{\sin x-1}{\sin x}\le 0\Rightarrow 0<\sin x\le 1 $
$ \Rightarrow x\in \underset{n\in I}{\mathop{\bigcup }},[2n\pi ,(2n+1)\pi ] $
BETA
