highschoolmom2010
  • highschoolmom2010
trigonometric functions
Mathematics
schrodinger
  • schrodinger
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highschoolmom2010
  • highschoolmom2010
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agent0smith
  • agent0smith
Well, you can start by testing a couple of values, to disprove it immediately try A=30 and B=59 Tan30 + tan59 = tan89 ?
terenzreignz
  • terenzreignz
I for one, do not recall the tangent identity to be quite as simple as tan(A) + tan(B) = tan(A + B)...

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agent0smith
  • agent0smith
It's not @terenzreignz, but the question states for A+B< 90 which makes it not able to be an identity. But it's easy to disprove.
terenzreignz
  • terenzreignz
Why not tan(45) + tan(30) = tan(75) :)
anonymous
  • anonymous
tan 45 = 1. tan 22.5 <> .5
agent0smith
  • agent0smith
^that also disproves it, @highschoolmom2010
anonymous
  • anonymous
basically tana+tanb= (sinacosb+sinbcosa)/cosacosb= sin(a+b)/cosacosb
terenzreignz
  • terenzreignz
At least we have exact values for these stuff :3 \[\Large \tan(45^o) = 1\\\Large \tan(30^o)=\frac1{\sqrt{3}}\]
agent0smith
  • agent0smith
My reasoning for picking a A+B close to 90, was due to tan90 being undefined, so it's highly unlikely two smaller angles will give anything close to the tangent of an angle near 90
anonymous
  • anonymous
=(sinacosb+cosasinb)/cosacosb=/= sinasinb/cosacosb
terenzreignz
  • terenzreignz
Noted :)
anonymous
  • anonymous
Now i need to somehow prove sinacosb+sinbcosa=/=sinasinb...
agent0smith
  • agent0smith
@katherine.ok based on her other questions, I don't think she's at the level of trigonometry where they're using proofs. I think it's more an analytical question.
anonymous
  • anonymous
tan 60 + tan (-30) <> tan 30
anonymous
  • anonymous
I think as simple as this sound...
anonymous
  • anonymous
by using the tangent graph, adding a random point where x is (0,90),you will not get tan a+ tan b because it is not linear graph.
agent0smith
  • agent0smith
^ good point.
highschoolmom2010
  • highschoolmom2010
im lost on all of this tbh....

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