Show that sin(x+pi)=-sinx. Show all of your work.

Answer 1

use the expansion equation
sin(A+B) = sinAcosB + cosAsinB

sin(x + π) = sinxcosπ + cosxsinπ
= sinx(-1) + cosx(0)
= -sinx

Answer 2

sin(xπi) = sinx cosπ + cosx sinπ

Answer 3

Thank you Reiny and oobleck!