Inverse Trigonometric Functions Question 121
Question: If $ \sin ( {{\sin }^{-1}}\frac{1}{5}+{{\cos }^{-1}}x )=1 $ , then what is x equal to?
Options:
A) 0
B) 1
C) $ \frac{4}{5} $
D) $ \frac{1}{5} $
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Answer:
Correct Answer: D
Let $ \sin [ {{\sin }^{-1}}( \frac{1}{5} )+{{\cos }^{-1}}x ]=1 $
$ \Rightarrow {{\sin }^{-1}}( \frac{1}{5} )+{{\cos }^{-1}}x={{\sin }^{-1}}1 $
$ \Rightarrow {{\sin }^{-1}}( \frac{1}{5} )+{{\cos }^{-1}}x=\frac{\pi }{2} $
$ \Rightarrow {{\cos }^{-1}}x=\frac{\pi }{2}-{{\sin }^{-1}}( \frac{1}{5} )={{\cos }^{-1}}( \frac{1}{5} ) $
$ \Rightarrow x=\frac{1}{5} $
BETA
