Question

$\left[\underset{x\to 2}{lim}{\sin }^{-1}\left(\sin \left(\frac{\sin (x^2-9x+14)}{\tan (x^2-5x+6)}\right)\right)\right]$ (where $[.]$ represents $GIF$) is equal to:

• A. $-2$
• B. $1$
• C. $0$
• D. $2$

Answer 1

The correct option is A $-2$

Given, $\left[\underset{x\to 2}{lim}{\sin }^{-1}\left(\sin \left(\frac{\sin (x^2-9x+14)}{\tan (x^2-5x+6)}\right)\right)\right]$

$L=\left[\underset{x\to 2}{lim}{\sin }^{-1}(\sin \left(\frac{\sin (x-2)(x-7)}{(x-2)(x-7)}\right)\frac{(x-2)(x-3)}{\tan (x-2)(x-3)}.\frac{(x-7)}{(x-3)})\right]$

$=\left[{\sin }^{-1}\right(\sin 5\left)\right]=[5-2\pi ]=-2$