The number of pairs (x,y) satisfying the equation sinx+siny=sin(x+y), |x|+|y|=1is
2
4
6
8
|x|+|y|−1|x|+|y|−1sin x+sin y−sin(x+y)⇒2sin(x+y2)cos(x−y2)−2sin(x+y2).cos(x+y2)⇒sin(x+y2)=0ORcos(x+y2)=cos(x−y2)x+y=0 OR ±(x−y2)=x+y2