Question

If 'x' takes negative permissible value, then $si{n}^{-1}x$ is equal to

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is A

$si{n}^{-1}=y$. then $x=siny$
since, $-1\le x<0,therefore-\frac{\pi }{2}\le si{n}^{-1}x<0$
$\Rightarrow -\frac{\pi }{2}\le y\le 0$
Now, $cosy=\sqrt{1-si{n}^{2}y}$
$\Rightarrow cosy=\sqrt{1-x^2}$ for $0\le y\le \pi$
But $-\frac{\pi }{2}\ge y>0$
$\Rightarrow cos(-y)=\sqrt{1-x^2}\Rightarrow -y=co{s}^{-1}\sqrt{1-x^2}$
$\Rightarrow -y=-co{s}^{-1}\sqrt{1-x^2}$
A liter let x = -1
Where, $0<t\le 1$
$\therefore sin-1x=si{n}^{-1}(-t)$
$=-co{s}^{-1}\sqrt{1-t^2}$
$=-co{s}^{-1}\sqrt{1-r^2}$