Chapter D, Problem 41E

(a)

To determine

To prove: The equation $\frac{1}{2}\left[\sin \left(x+y\right)+\sin \left(x-y\right)\right]=\sin x\cos y$.

(b)

To determine

To prove: The equation $\frac{1}{2}\left[\cos \left(x+y\right)+\cos \left(x-y\right)\right]=\cos x\cos y$.

(c)

To determine

To prove: The equation $\frac{1}{2}\left[\cos \left(x-y\right)-\cos \left(x+y\right)\right]=\sin x\sin y$.