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On an inequality of a product function

Posted: Tue Aug 22, 2017 9:07 am
by Riemann
Let

$$f(x) = \sin x \sin (2x) \sin (4x) \cdots \sin (2^n x)$$

Prove that

$$\left| {f(x)} \right| \le \frac{2}{{\sqrt 3 }}\left| {f(\frac{\pi }{3})} \right|$$