Given, sin^-1 (-√3/2) + cos^-1 (-1/2)

= - sin^-1 (√3/2) + cos^-1 (1/2)               {since sin^-1 (-x) = -sin^-1 x and cos^-1 (-x) = cos^-1 x, -1 ≤ x ≤ 1}

= -π/3 + π/3                                         {since sin π/3 = √3/2 and cos π/3 = 1/2}

= 0

So, sin^-1 (-√3/2) + cos^-1 (-1/2) = 0