Use the that |sin(x)|≤|x| and the formula that makes sin(x)-sin(y) in a product to demonstrate that |sin(x)-sin(y)|≤|x-y|

This is what i have, but i can't go further, I'm desperate, i will be even more desperate because the work has 11 problems that subdivide, and I am a total useless, so please if someone could help me only with this one