Question

The sum of roots of the equation $si{n}^{-1}x-co{s}^{-1}x=si{n}^{-1}(3x-2)$ is

• A. $3/2$
• B. $1$
• C. $1/2$
• D. $2$

Answer 1

The correct option is A $3/2$

$2{\sin }^{-1}\left(x\right)-\frac{\pi }{2}={\sin }^{-1}(3x-2)$
$3x-2=-\cos \left(2{\sin }^{-1}\right(x\left)\right)$
$3x-2=-(1-2{\sin }^2({\sin }^{-1}\left(x\right)\left)\right)$
$3x-2=-1+2x^2$
$2x^2-3x+1=0$
$x^2-\frac{3}{2}x+\frac{1}{3}=0$
Hence sum of roots will be $\frac{3}{2}$.