Proving inequalities - Does induction work?? 1. The problem statement, all variables and given/known data prove that, for a,b,c>0, a+b+c=1, 1/a+1/b+1/c≥9 2. Relevant equations it says that i might want to use the fact that for all X=/=0, X+1/X ≥ 2 3. The attempt at a solution using the tip I could make it: a+1/a+b+1/b+c+1/c ≥ 10 but that's as far as I got. 1. The problem statement, all variables and given/known data prove using induction (or anything else): |sin(nx)|≤n|sin(x)| for natural n 2. Relevant equations 3. The attempt at a solution well it's true for n=1 after using the induction assumption I made it so I have to prove that: |sin(x(n+1))|≤|sin(nx)| + |sin(x)| now i'm suck, I don't see how I could use trigonometry equivalences since they all give me cosins and sins*cosins and stuff like that, and these absolute values are a pain aswell, I could square it here and there, to get rid of them, but I don't see where it's going again.