mathslover
  • mathslover
tan A = -1/2 , tan B = -1/3 , then A+B = ?
Trigonometry
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SOLVED
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schrodinger
  • schrodinger
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mathslover
  • mathslover
@calculusfunctions sir.
mathslover
  • mathslover
I had come up with : tan (A+B) = -1
mathslover
  • mathslover
so (A+B) = ?

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More answers

anonymous
  • anonymous
A+B = -45 + 180 * k
mathslover
  • mathslover
is it, 7pi /4
anonymous
  • anonymous
\[\tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \cdot \tan(B)}\]
anonymous
  • anonymous
-45 = pi/4 180 = pi so -pi/4 + pi = 3pi/4 -pi/4 + 2pi = 7pi/4 and so on..
anonymous
  • anonymous
If you calculated it right then: \[A+B= \tan^{-1}(-1)\]
anonymous
  • anonymous
so 7pi/4 is one possibility
anonymous
  • anonymous
\[A+B = \tan^{-1}\frac{ -1 }{ 2 }+\tan^{-1} \frac{ -1 }{ 3 }\]
mathslover
  • mathslover
so it can be : 3 pi / 4, 7pi/4 , . ... It can not be 5 pi / 4 because it will be positive for tan.
mathslover
  • mathslover
But the book says that the answer is : d) none Options were : i) pi/4 ii) 3 pi/4 iii) 5 pi/4 iv) none.
mathslover
  • mathslover
So it will be 3 pi/4 ? or none?
hartnn
  • hartnn
it will be 3pi/4 are any constraints given?
mathslover
  • mathslover
constraints?
hartnn
  • hartnn
like A+B should be between 0 to 90 or something like this ?
hartnn
  • hartnn
else 3pi/4 is correct
mathslover
  • mathslover
ok thanks a lot @hartnn :)
anonymous
  • anonymous
wud tan(A+B) formula work for all angles
hartnn
  • hartnn
yes.
anonymous
  • anonymous
ok thank you :D
anonymous
  • anonymous
\[\pi - \frac{\pi}{4} = \frac{3 \pi}{4}\]
anonymous
  • anonymous
There was some mistake in the formula that I had written above.. That day I was looking for the same and now I have found it : \[\tan^{-1}(-x) = \pi - \tan^{-1}(x)\]

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