Question

Assertion :The equation $2{\left({\sin }^{-1}x\right)}^2-5({\sin }^{-1}x+2)=0$ Reason: ${\sin }^{-1}\left(\sin x\right)=xifxϵ[-1.57,1.57]$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion false but Reason is true

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$2{\left({\sin }^{-1}x\right)}^2-5\left({\sin }^{-1}x\right)+2=0$

$\Rightarrow {\sin }^{-1}x=\frac{5\pm \sqrt{25-16}}{4}=2,\frac{1}{2}$

$\Rightarrow {\sin }^{-1}x=\frac{1}{2},{\sin }^{-1}x=2$

$\therefore x=\sin \left(\frac{1}{2}\right)andx={\sin }^{-1}2$ is not possiable

$\therefore x=\sin \left(\frac{1}{2}\right)$ is only solution

$\therefore$ Assertion (A) is false.