The question to to prove that abs(sin(x)-sin(y)) < (or equal to) abs(x-y). Here's what I have so far: abs(sin(x)-(sin(y)) = 2 sin((x-y)/2) cos ((x-y)/2) = 2 sqrt((1-cos(x-y))/2) sqrt ((1+cos(x-y))/2) I am unsure at how to go forward.