The number of ordered pairs (x,y) satisfying the system of equations given by sinx+cosx=sin(x+y) and |x|+|y|=1 is???

sin x + sin y = 2 sin ((x+y)/2))cos((x-y)/2)

sin(x+y) = 2 sin ((x+y)/2))cos((x+y)/2)

cos((x-y)/2) = cos((x+y)/2)

cos((x-y)/2) - cos((x+y)/2) =0

2sin(x/2)sis(y/2) = 0 (we converted difference of cosines into a product).

x=0 or y=0.

So, there are four answers (0,1), (0,-1), (1,0), (-1,0).