If x+1/x=2, then principal value of sin^-1x is :

The correct answer is Option (3) → $\frac{\pi }{2}$

$x+\frac{1}{x}=2$

so $\frac{x^2+1}{x}=2$

so $x^2+1=2x$

$x^2-2x+1=0⇒(x-1)^2=0⇒x=1$

$\sin^{-1}(1)=\frac{\pi }{2}$