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Sunday, November 30, 2008

A trigonometric identity

\tan(a)+\tan(b)+\tan(c)\tan(a)*\tan(b)*\tan(c) \\ ( a+b+c=180^{\circ} )

Isn't that beautiful? ( Can you prove it? )


  1. You're right. That is beautiful. I'd never seen that before.

    You inspired me to write a post this afternoon about the converse to that identity.

  2. ummm ... a, b, and c are the angles of a single triangle.

    i learned this here.

  3. oh. heck. there it is
    right in your post:
    a + b + c = 180^\circ.

    so my attempt at a correction
    was misguided. i really *did*
    learn this at polymath, though ...

  4. Start off with tan(a+b)=tan(\pi-c)=-tan(c). Then expand tan(a+b) using the additive identity. It follows easily from there.


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