Problem 1564 (difficulty: 3/10)

Prove that

\(\displaystyle \sin (z_1+z_2)=\sin z_1\cos z_2+\cos z_1\sin z_2\)

and

\(\displaystyle \cos(z_1+z_2)=\cos z_1\cos z_2-\sin z_1\sin z_2.\)

Give me another random problem!