Power-reduction Formula
Obtained by solving the second and third versions of the cosine double-angle formula.
| Sine | Cosine | Other |
|---|---|---|
and in general terms of powers of sin θ or cos θ the following is true, and can be deduced using De Moivre's formula, Euler's formula and binomial theorem.
| Cosine | Sine | |
|---|---|---|
Read more about this topic: List Of Trigonometric Identities
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“Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective positions of the beings which compose it, if moreover this intelligence were vast enough to submit these data to analysis, it would embrace in the same formula both the movements of the largest bodies in the universe and those of the lightest atom; to it nothing would be uncertain, and the future as the past would be present to its eyes.”
—Pierre Simon De Laplace (1749–1827)