On an inequality of a product function
Posted: Tue Aug 22, 2017 9:07 am
Let
$$f(x) = \sin x \sin (2x) \sin (4x) \cdots \sin (2^n x)$$
Prove that
$$\left| {f(x)} \right| \le \frac{2}{{\sqrt 3 }}\left| {f(\frac{\pi }{3})} \right|$$
$$f(x) = \sin x \sin (2x) \sin (4x) \cdots \sin (2^n x)$$
Prove that
$$\left| {f(x)} \right| \le \frac{2}{{\sqrt 3 }}\left| {f(\frac{\pi }{3})} \right|$$