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sin(x) = 2sin(x/2)cos(x/2)

sin(x/2) = 2sin(x/4)cos(x/4)

sin(x/4) = 2sin(x/8)cos(x/8) ...

So we can arrive at this

[tex] \sin{x} = 2^n \cdot \sin{\left(\frac{x}{2^n}\right)} \prod_{k=1}^{n} \cos{\left(\frac{x}{2^k}\right)} [/tex]

Valid for [tex] n \in \mathbb{N} \backslash \{ 0 \} [/tex]

Can you use this formula for anything?

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# Sin product

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