0＜(X+Y)/2＜π、-π/2＜(X-Y)/2＜π/2
sinX+sinY=2sin{(X+Y)/2}cos{(X-Y)/2}
2sin{(X+Y)/2}-2sin{(X+Y)/2}cos{(X-Y)/2}=2sin{(X+Y)/2}{1-cos{(X-Y)/2}}≧0
sinX+sinY≦2sin{(X+Y)/2}