We know that, sin(x+y)=sinxcosy+cosxsiny --------(i) and sin(x−y)=sinxcosy−cosxsiny --------(ii) Adding equations (i) and (ii), we get : sin(x+y)+sin(x−y)=2sinxcosy -----(iii) Let x+y=C and x−y=D ⇒ x=
C+D
2
y=
C−D
2
Substituting above values in equation (iii) ⇒ sinC+sinD=2sin(