Inverse Trigonometric Functions Question 230
Question: If $ {{\sin }^{-1}}x+{{\cot }^{-1}}( \frac{1}{2} )=\frac{\pi }{2}, $ then x is
[Roorkee 1999; Karnataka CET 1999]
Options:
A) 0
B) $ \frac{1}{\sqrt{5}} $
C) $ \frac{2}{\sqrt{5}} $
D) $ \frac{\sqrt{3}}{2} $
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Answer:
Correct Answer: B
Solution:
$ \because $
$ {{\cot }^{-1}}\frac{1}{2}={{\cos }^{-1}}\frac{1}{\sqrt{5}} $ Hence given equation can be written as $ {{\sin }^{-1}}x+{{\cos }^{-1}}\frac{1}{\sqrt{5}}=\frac{\pi }{2} $
$ \Rightarrow $ $ x=\frac{1}{\sqrt{5}} $ .
BETA
