| sinx |
| cosx |
∴sinx=xcosx
同理，siny=ycosy
所以原式=
| sinxcosy+cosxsiny |
| x+y |
| sinxcosy−cosxsiny |
| x−y |
=
| xcosxcosy−ycosxcosy |
| x−y |
| xcosxcosy+ycosxcosy |
| x+y |
=
| cosxcosy(x+y) |
| x+y |
| cosxcosy(x−y) |
| x−y |
=cosxcosy-cosxcosy
=0
故答案为：0
| sin(x+y) |
| x+y |
| sin(x−y) |
| x−y |
| sinx |
| cosx |
| sinxcosy+cosxsiny |
| x+y |
| sinxcosy−cosxsiny |
| x−y |
| xcosxcosy−ycosxcosy |
| x−y |
| xcosxcosy+ycosxcosy |
| x+y |
| cosxcosy(x+y) |
| x+y |
| cosxcosy(x−y) |
| x−y |