# Newton a fraud?

**URL:** <https://boards.straightdope.com/t/newton-a-fraud/957280>\
**Category:** In My Humble Opinion\
**Created:** [January 5, 2022, 8:49pm UTC](https://boards.straightdope.com/t/newton-a-fraud/957280 "2022-01-05T20:49:07Z")\
**Posts on this page:** 2\
**Page:** 4

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**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\
**Post date:** [January 17, 2022, 3:31am UTC](https://boards.straightdope.com/t/newton-a-fraud/957280/74 "2022-01-17T03:31:49Z")

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That’s how I dealt with a lot of trig identities - sin(x+y) equals some sum of products of sins and cosines - let’s try x=15 degrees and y=30 degrees (with my calculator) and see what makes sense.

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**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\
**Post date:** [January 17, 2022, 3:57am UTC](https://boards.straightdope.com/t/newton-a-fraud/957280/75 "2022-01-17T03:57:17Z")

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In one dimension, two nonequivalent polynomials can only coincide at a finite number of points, so picking a random point has a 100% chance of revealing whether the expressions are equivalent or not (let’s say over the complex numbers, not a finite field or anything like that). In higher dimensions, meaning more than 1 variable, you should still be OK since an algebraic hypersurface will have strictly smaller dimension than the entire space, so all you have to do is pick a random value for each variable.

Trigonometric identities basically amount to checking polynomials, since \sin x = (e^{ix}-e^{-ix})/2i and so on.

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