anonymous
  • anonymous
Given tan A + tan B = 3x and tan A tan B = 2x^2 How to find tan A - tan B ?
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@ganeshie8
anonymous
  • anonymous
from your 2nd equation, \[\tan(B)=\frac{2x^2}{\tan(A)}\] Put this in 1st equation \[\tan(A)+\frac{2x^2}{\tan(A)}=3x\] Multiply by tan(A) \[\tan^2(A)+2x^2=3x.\tan(A)\]\[\tan^2(A)-3x.\tan(A)+2x^2=0\] Split \[-3x=-x-2x\] and simplify to get tan(A) in terms of x, use the value of tan(A) in terms of x to get tan(B) in terms of x then evaluate tan(A)-tan(B) in terms of x
ParthKohli
  • ParthKohli
I swear to God I just saw this question on Math.SE.

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anonymous
  • anonymous
@Nishant_Garg uhh.. how can you split that way when you have 2 unknowns.. ?
anonymous
  • anonymous
@ParthKohli Hi Professor, what is Math.S.E ? can you kindly help me out on this ? ><
ParthKohli
  • ParthKohli
\[(\tan A - \tan B) ^2 = (\tan A + \tan B)^2 - 4\tan A \tan B \]
ParthKohli
  • ParthKohli
Someone asked exactly the same question on another side, and the difference is only of a minute or two.
anonymous
  • anonymous
The answer will still be in terms of x only?or am I missing something?
anonymous
  • anonymous
@ParthKohli now thats a equation we dont see often :| @Nishant_Garg yup! answer in terms of x
ParthKohli
  • ParthKohli
\[(\tan A - \tan B)^2 = (3x)^2 - 4(2x)^2 = x^2\]\[\tan A - \tan B =x \]
ParthKohli
  • ParthKohli
You do understand what that equation means though, right?
anonymous
  • anonymous
@ParthKohli oh yes i got it! thank you so much!! :D
ParthKohli
  • ParthKohli
Note that the answer can also be \(-x\).
anonymous
  • anonymous
Yep I got \[\pm x\] from my method
ParthKohli
  • ParthKohli
It was pretty visible too. \[x + 2x = 3x\]and\[x\cdot 2x = 2x^2\]

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