The first equation can be written as
when sin 1/2(x + y) = 0 we have that either sin 1/2 x = 0 or sin 1/2 y = 0.Therefore, either sin 1/2(x + y) = 0 or cos 1/2(x + y) = 0.
⇒ x + y = 0, or x = 0 or y = 0. As |x| + |y| = 1, therefore when x + y = 0, we have to reject x + y = 1, or x + y = -1 and solve it with x − y = 1 or x - y = -1 which gives (1/2,-1/2) or (-1/2,1/2) as the possible solution. Again solving with x = 0, we get (± 1,0), and solving with y = 0, we get (±1 ,0) as the other solution. Thus, we have six pairs of solution for x and y.