Math-Trigonometry

Show that if A, B, and C are the angles of an acute triangle, then tan A + tan B + tan C = tan A tan B tan C.
I tried drawing perpendiculars and stuff but it doesn't seem to work?
For me, the trig identities don't seem to plug in as well.
Help is appreciated, thanks.

asked by Sam
  1. C = 180-(A+B), so
    tan C = -tan(A+B) = (tanA+tanB)/(tanAtanB-1)

    tanA+tanB+tanC
    = tanA+tanB + (tanA+tanB)/(tanAtanB-1)
    = (tanA+tanB)(1 + 1/(tanAtanB-1))
    = (tanA+tanB)(tanAtanB)/(tanAtanB-1)
    = (tanAtanB)(tanA+tanB)/(tanAtanB-1)
    = tanAtanBtanC

    posted by Steve
  2. Thanks a ton!

    posted by Sam

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