| Assertion [A]: The principal value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)=\frac{\pi }{3}\] |
| Reason [R]: The range of \[{{\cos }^{-1}}x\] is \[\left[ 0,\,\,\pi \right]\] |
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 :
\[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)={{\cos }^{-1}}\left( \cos \left( 2\pi -\frac{\pi }{3} \right) \right)={{\cos }^{-1}}\left( \cos \frac{\pi }{3} \right)\] Here both statements are true R is the correct explanation of Assertion A. \[\therefore \]Option [A] is the correct answer.
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