How do I prove that sin (x + pi) = -sin x?

To prove that sin(x + pi) = -sin x, use the expansion for
sin(a + b).

sin(a + b) = sin a * cos b + cos a * sin
b

sin(x + pi)

=> sin x
* cos pi + cos x * sin pi

sin pi = 0 and cos pi =
-1

=> sin x * (-1) + cos x *
0

=> - sin
x

This proves that sin ( x + pi) = - sin
x