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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 ?
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0from 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 \[3x=x2x\] 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
 one year ago
Best ResponseYou've already chosen the best response.2I swear to God I just saw this question on Math.SE.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Nishant_Garg uhh.. how can you split that way when you have 2 unknowns.. ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ParthKohli Hi Professor, what is Math.S.E ? can you kindly help me out on this ? ><

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2\[(\tan A  \tan B) ^2 = (\tan A + \tan B)^2  4\tan A \tan B \]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2Someone asked exactly the same question on another side, and the difference is only of a minute or two.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The answer will still be in terms of x only?or am I missing something?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ParthKohli now thats a equation we dont see often : @Nishant_Garg yup! answer in terms of x

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2\[(\tan A  \tan B)^2 = (3x)^2  4(2x)^2 = x^2\]\[\tan A  \tan B =x \]

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2You do understand what that equation means though, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ParthKohli oh yes i got it! thank you so much!! :D

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2Note that the answer can also be \(x\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep I got \[\pm x\] from my method

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2It was pretty visible too. \[x + 2x = 3x\]and\[x\cdot 2x = 2x^2\]
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