Double Angle Formulas/Sine/Proof 2

Theorem

$\sin 2 \theta = 2 \sin \theta \cos \theta$


Proof

\(\ds \sin 2 \theta\) \(=\) \(\ds \map \sin {\theta + \theta}\)
\(\ds \) \(=\) \(\ds \sin \theta \cos \theta + \cos \theta \sin \theta\) Sine of Sum
\(\ds \) \(=\) \(\ds 2 \sin \theta \cos \theta\)

$\blacksquare$


Sources

  • 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: The addition formulae
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.