| Directions : (1 - 10) |
| The following questions consist of two statements, one labelled as "Assertion [A] and the other labelled as Reason [R]". You are to examine these two statements carefully and decide if Assertion [A] and Reason [R] are individually true and if so, whether the Reason [R] is the correct explanation for the given Assertion [A]. Select your answer from following options. |
| Assertion [A]: The principal value of \[{{\sin }^{-1}}\left( -\frac{1}{2} \right)\] is \[-\frac{\pi }{6}\]. |
| Reason [R]: The principal value of \[{{\sin }^{-1}}\left( -x \right)\] is \[-{{\sin }^{-1}}x\] if \[x\in \left[ -1,\,\,1 \right]\] |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: A
Solution :
\[{{\sin }^{-1}}\left( -\frac{1}{2} \right)={{\sin }^{-1}}\left( -\sin \frac{\pi }{6} \right)={{\sin }^{-1}}\left( \sin \left( -\frac{\pi }{6} \right) \right)=-\frac{\pi }{6}\] Here both statements are true and Statement R is the correct explanation of statement A. \[\therefore \]Option [A] is the Correct answer.
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