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Morrie's law is a name, that occasionally is used for the trigonometric identity## References

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- $cos(20^circ)\; cdot\; cos(40^circ)\; cdot\; cos(80^circ)=frac\{1\}\{8\}.$

It is a special case of the more general identity

- $2^n\; cdot\; prod\_\{k=0\}^\{n-1\}\; cos(2^k\; alpha)=frac\{sin(2^n\; alpha)\}\{sin(alpha)\}$

with n = 3 and α = 20°. The name is due to the physicist Richard Feynman, who used to refer to the identity under that name. Feynman picked that name, because he learned it during his childhood from a boy with the name Morrie Jacobs and afterwards remembered it for all of his life.

A similar identity for the sine function also holds:

- $sin(20^circ)\; cdot\; sin(40^circ)\; cdot\; sin(80^circ)=frac\{sqrt\; 3\; \}\{8\}.$

Moreover, dividing the second identity by the first, the following identity is evident:

- $tan(20^circ)\; cdot\; tan(40^circ)\; cdot\; tan(80^circ)=sqrt\; 3\; =tan(60^circ).$

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Last updated on Monday September 22, 2008 at 18:12:04 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday September 22, 2008 at 18:12:04 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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