Let x + (1)/(x) = 2, y + (1)/(y) = - 2 and ^ - 1 x + ^ - 1 y = mπ ,...

$x + \dfrac{1}{x} = 2 ⇒ x = 1$ $\ldots . [ x + \dfrac{1}{x} \ge 2$ as equality occurs only when $x = 1 ]$
$⇒ \sin^{- 1}x = \dfrac{\pi}{2}$

Similarly, $y = - 1$ $. . . . [ y + \dfrac{1}{y} \le - 2$ as equality occurs only when $y = - 1 ]$
$⇒ \cos^{- 1}y = \pi$
$\sin^{- 1}x + \cos^{- 1}y = \dfrac{\pi}{2} + \pi$
$= \dfrac{3\pi}{2}$
$⇒ m = \dfrac{3}{2} = 1.5$