Show that sin(x+pi)=-sinx Show all of your work
To prove that sin(x+pi) = -sinx, we will use the angle sum formula for sine:
sin(a+b) = sin a cos b + cos a sin b
Let a = x and b = pi:
sin(x + pi) = sin x cos pi + cos x sin pi
Recall that cos(pi) = -1 and sin(pi) = 0:
sin(x + pi) = sin x * (-1) + cos x * 0
sin(x + pi) = -sin x
Therefore, sin(x + pi) = -sin x.