Trig Square Product

Geometry Level 3

∏ k = 0 n sin ⁡ 2 ( 2 k x ) ≤ ( 3 4 ) n \prod_{k=0}^{n} \sin^2(2^k x) \le \left(\dfrac{3}{4}\right)^n

Does the inequality above hold true for all natural number n n and all real x x ?

Source: Gaokao 2020, II

Yes No

Alice Smith by Alice Smith , 20, China

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1 solution

Callie Ferguson
Oct 13, 2020

I graphed this out on geogebra and explained how I got the answer. Here's the link: Geogebra Solution

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