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ehrenfest
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Homework Statement
For all x in the interval [tex] 0 \leq x \leq \pi [/tex], prove that [tex]|\sin{nx}| \leq n\sin{x}[/tex]
where n is a nonnegative integer.
Homework Equations
The Attempt at a Solution
It is obviously true for n=0. Assume this result is true for n=k. Then
[tex]|\sin(k+1)x| = |\sin kx \cos x + \sin x \cos kx | [/tex]
and I am not sure what to do with that. I think the fact that cosine is nonnegative in this interval might be useful.
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