Trigonometry/Price's Theorem

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Price's Theorem states that as

.

Lemma

As Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "/mathoid/local/v1/":): {\displaystyle n \rightarrow \inf, \, 2^n \sin \left (\frac{\theta}{2^n} \right ) \rightarrow \theta} .

Proof of lemma

As hence . Rearranging, the result follows.

Proof of theorem

Thus

The result then follows from the lemma.

This theorem is due to Bartholomew Price (1818-1898).