| Direction: For the following questions, chose the correct answer from the codes [a], [b] [c] and [d] defined as follows. |
| Using the identity \[{{\sin }^{-1}}(\sin \,x)\,=x,\,\frac{\pi }{2}\le x\le \frac{\pi }{2}\]. |
| Statement I\[{{\sin }^{-1}}(\sin \,2)=2\] |
| Statement II The principal value of \[{{\sin }^{-1}}\,(\sin \,x)=x\] |
A) Statement I is true, Statement II is also true and Statement II is the correct explanation of Statement I.
B) Statement I is true, Statement II is true and Statement II is not the correct explanation of Statement I.
C) Statement I is true, Statement II is false.
D) Statement I is false, Statement II is true.
Correct Answer: D
Solution :
\[\therefore \] \[{{\sin }^{-1}}\,(\sin \,2)\,={{\sin }^{-1}}\,(\sin \,(\pi -2))=\pi -2\] \[\therefore \] Statement I is false. and \[{{\sin }^{-1}}\,(\sin \,x)\,=x,\,\,\forall \,x\,\in \,\left[ -\frac{\pi }{2},\,\,\frac{\pi }{2} \right]\]
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