Problem: Simplify sin(x−y)cosy+cos(x−y)siny\sin (x-y) \cos y+\cos (x-y) \sin ysin(x−y)cosy+cos(x−y)siny.
Answer Choices:
A. 111
B. sinx\sin xsinx
C. cosx\cos xcosx
D. sinxcos2y\sin x \cos 2 ysinxcos2y
E. cosxcos2y\cos x \cos 2 ycosxcos2y
Solution:
Let w=x−yw=x-yw=x−y. Then the given expression is sinwcosy+coswsiny=\sin w \cos y+\cos w \sin y=sinwcosy+coswsiny= sin(w+y)=sinx\sin (w+y)=\sin xsin(w+y)=sinx.