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Double angle identities

The trigonometric double-angle identities are easily derived from the angle addition formulas by just letting $x = y$. Doing so yields:

  • $\sin (2x) = 2\sin (x) \cos (x)$
  • $\cos (2x) = \cos^2 (x) - \sin^2 (x)$
  • $\tan (2x) = \frac{2\tan (x)}{1-\tan^2 (x)}$

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Proof

Please try to prove it on your own.

See Also

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