Question

Solve for x and y:

sin^-1x + sin^-1y = 2π/3, cos^-1x - cos^-1y = π/3.

Answer 1

Given equations are

sin^-1x + sin^-1y = 2π/3, ...(i)

cos^-1x - cos^-1y = π/3  ....(ii)

(i) reduces to

⇒ π/2 - cos^-1x + π/2 - cos^-1y = 2π/3

π - (cos^-1x + cos^-1y) = 2π/3

⇒ (cos^-1x + cos^-1y) = π - 2π/3 = π/3 ....(iii)

Adding (ii) and (iii), we get

2cos^-1x = 2π/3

⇒ cos^-1x = π/3

⇒ x = cos(π/3) = 1/2

when x = 1/2, y = 0

Hence, the solutions are x = 1/2 and y = 0.