7.5 Simplify $\sin (x-y) \cos y+\cos (x-y) \sin y$, its value is
(A) 1.
(B) $\sin x$.
(C) $\cos x$.
(D) $\sin x \cos y$.
(E) $\cos x \cos 2 y$.
(34th American High School Mathematics Examination, 1983)
[Solution] Let $w=x-y$, then the given expression can be transformed into
$\sin w \cos y+\cos w \sin y=\sin (w+y)=\sin (x-y+y)=\sin x$. Therefore, the correct choice is $(B)$.