Question

Given tan A + tan B = 3x and tan A tan B = 2x^2 How to find tan A - tan B ?

Answer 1

@ganeshie8

Answer 2

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

Answer 3

I swear to God I just saw this question on Math.SE.

Answer 4

@Nishant_Garg uhh.. how can you split that way when you have 2 unknowns.. ?

Answer 5

@ParthKohli Hi Professor, what is Math.S.E ? can you kindly help me out on this ? ><

Answer 6

\[(\tan A - \tan B) ^2 = (\tan A + \tan B)^2 - 4\tan A \tan B \]

Answer 7

Someone asked exactly the same question on another side, and the difference is only of a minute or two.

Answer 8

The answer will still be in terms of x only?or am I missing something?

Answer 9

@ParthKohli now thats a equation we dont see often :|
@Nishant_Garg yup! answer in terms of x

Answer 10

\[(\tan A - \tan B)^2 = (3x)^2 - 4(2x)^2 = x^2\]\[\tan A - \tan B =x \]

Answer 11

You do understand what that equation means though, right?

Answer 12

@ParthKohli oh yes i got it! thank you so much!! :D

Answer 13

Note that the answer can also be \(-x\).

Answer 14

Yep I got \[\pm x\]
from my method

Answer 15

It was pretty visible too. \[x + 2x = 3x\]and\[x\cdot 2x = 2x^2\]