| Assertion [A]: The principal value, of \[{{\tan }^{-1}}\left( \tan \frac{3\pi }{4} \right)\] is \[-\frac{\pi }{4}\]. |
| Reason [R]: The range of \[{{\tan }^{-1}}x\] is \[\left[ \frac{-\pi }{2},\,\frac{\pi }{2} \right]\]. |
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 :
\[{{\tan }^{-1}}\left( \tan \frac{3\pi }{4} \right)={{\tan }^{-1}}\left( \tan \left( \pi -\frac{\pi }{4} \right) \right)={{\tan }^{-1}}\left( -\tan \frac{\pi }{4} \right)\] \[=-\frac{\pi }{4}\] and Range of \[{{\tan }^{-1}}x\] is \[\left( \frac{-\pi }{2},\,\frac{\pi }{2} \right)\]. Here Assertion [A] is true and Reason [R] is not correct explanation of statement A. \[\therefore \]Option [A] is the correct answer.
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