(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate for [tex]x\in(0,\pi/2)[/tex]

[tex]\lim_{N\rightarrow\infty}\prod_{n=0}^{N}cos(\frac{x}{2^{n}})[/tex]

Hint: Use the Double-Angle Formulas for the sine.

2. Relevant equations

3. The attempt at a solution

[tex]cos(x)\cdot cos(\frac{x}{2})\cdot cos(\frac{x}{4})\cdot...[/tex]

[tex]\frac{\sin2x}{2\cdot\sin x}\cdot\frac{\sin x}{2\cdot\sin x/2}\cdot\frac{\sin x/2}{2\cdot\sin x/4}\cdot...[/tex]

[tex]\frac{\sin2x}{2}\cdot\frac{1}{2}\cdot\frac{1}{2}\cdot...\cdot\frac{1}{2\cdot\sin x/N}[/tex]

[tex]\frac{\sin2x}{\sin(x/{2^N})\cdot2^{N}}[/tex]

However, now I have to resolve the 0*infinity in the denom. But how do I resolve that.

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# Homework Help: Limit of a product cos

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