• question_answer 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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