Letasolution y = y(x) of the differential equation
$$x\sqrt{x^2 - 1} dy - y\sqrt{y^2 - 1}dx = 0$$ satisfy $$y(2) = \frac{2}{\sqrt{3}}$$
STATEMENT-1: $$y(x) = \sec\left(\sec^{-1}x - \frac{\pi}{6}\right)$$
STATEMENT-2: y(x) is given by $$\frac{1}{y} = \frac{2\sqrt{3}}{x} - \sqrt{1 - \frac{1}{x^2}}$$

A

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

B

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1

C

STATEMENT-1 is True, STATEMENT-2 is False

D

STATEMENT-1 is False, STATEMENT-2 is True