| Assertion [A]: The principal value of \[{{\cos }^{-1}}\left( \frac{-1}{\sqrt{2}} \right)\] is \[-\frac{\pi }{4}\] |
| Reason [R]: The principal value of \[{{\cos }^{-1}}\left( -x \right)\] is \[\pi -{{\cos }^{-1}}x\] 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: D
Solution :
\[{{\cos }^{-1}}\left( \frac{-1}{\sqrt{2}} \right)=\pi -{{\cos }^{-1}}\frac{1}{\sqrt{2}}=\pi -\frac{\pi }{4}=\frac{3\pi }{4}\] Here statement A is false and statement R is true \[\therefore \]Option [D] is the correct answer.
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