MathTrigonometry
posted by Sam .
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.

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)
= tanAtanBtanC 
Thanks a ton!
Respond to this Question
Similar Questions

Integration
Intergrate ¡ì sec^3(x) dx could anybody please check this answer. are the steps correct? 
calculus
can anyone tell me if tan1x= 1 over tan x? 
Trigonometry
Hello, everyone: I am working on finding the exact values of angles that are less common and are therefor not found easily on the Unit Circle (at least, they are not labeled). For example, the problem I am asking about is: 10) Find … 
Trig  tan 15° using composite argument?
tan 15° tan (45°30°) (tan 45°  tan 30°)/1+ tan 45°tan30° (1√3/3)/(1+1√3/3) then i donnt what to do/ chancel out. Can someone finish it if i didn't get it wrong. thanks in advance 
trig
h t t p : / / i m g 4 0 . i m a g e s h a c k . u s / c o n t e n t . p h p ? 
Trig.
sec^2xcotxcotx=tanx (1/cos)^2 times (1/tan)(1/tan)=tan (1/cos^2) times (2/tan)=tan (2/cos^2tan)times tan=tan(tan) sq. root of (2/cos^2)= sq. root of (tan^2) sq. root of (2i)/cos=tan I'm not sure if I did this right. If I didn't, … 
Trigonometry
Find the exact value of tan(ab) sin a = 4/5, 3pi/2<a<pi; tan b = sqrt2, pi/2<b<pi identity used is: tan(ab)=(tan atan b)/1+tan a tan b simplify answer using radicals. (a is alpha, b is beta) 
precalculus
For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1tan(x)) c. (cos(x+y))/(cos(xy))= (1tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) … 
Math Precalculus
Write the expression as the sine, cosine, tangent of an angle (in radians.) (tan(pi/5)tan(pi/3))/(1+tan(pi/5)tan(pi/3)) 
calculus
If limit as delta x approaches 0 of tan(0+Δx)tan(0)/Δx =1 which of the following is false: d/dx [tanx]=1 the slope of y = tan(x) at x = 0 is 1 y = tan(x) is continuous at x = 0 y = tan(x) is differentiable at x = 0