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## anonymous one year ago Given tan A + tan B = 3x and tan A tan B = 2x^2 How to find tan A - tan B ?

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1. anonymous

@ganeshie8

2. 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

3. ParthKohli

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

4. anonymous

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

5. anonymous

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

6. ParthKohli

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

7. ParthKohli

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

8. anonymous

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

9. anonymous

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

10. ParthKohli

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

11. ParthKohli

You do understand what that equation means though, right?

12. anonymous

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

13. ParthKohli

Note that the answer can also be $$-x$$.

14. anonymous

Yep I got $\pm x$ from my method

15. ParthKohli

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

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