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How can I prove

$$\lim_{n\to\infty} \cos(\alpha/n)^{2n}=1$$

for all ##\alpha\in\mathbb{R}##? The physical background is Malus' law for perfect linear polarizers, I'd like to show that one can losslessly rotate a linearly polarized wave by any angle by stacking an infinite number of infinitely rotated polarizers.

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# I Malus' law in the limit of infinitely many polarizers

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