I did not try to do the problem yet but you can use the fact that,Originally Posted by Nichelle14
Thus, you need to prove that,
If and only if,
Mathematical induction is the tool here.
It is true for thus, there is a such as,
Thus,
But,
Thus, (mutiply inequalities notice they are non-negative),
......(1)
Also,
And,
Thus, (mutiply inequalites notice they are non-negative),
......(2)
Using the property on (1) and (2) we have,
Now, add these inequalities,
Now, by triangular inequality,
By transitivity ( ),
Thus, recognizing the sum for sine and simply the right side,
Proof is complete.