MathTrigonometry
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

C = 180(A+B), so
tan C = tan(A+B) = (tanA+tanB)/(tanAtanB1)
tanA+tanB+tanC
= tanA+tanB + (tanA+tanB)/(tanAtanB1)
= (tanA+tanB)(1 + 1/(tanAtanB1))
= (tanA+tanB)(tanAtanB)/(tanAtanB1)
= (tanAtanB)(tanA+tanB)/(tanAtanB1)
= tanAtanBtanCposted by Steve

Thanks a ton!
posted by Sam
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