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mathslover

tan A = -1/2 , tan B = -1/3 , then A+B = ?

  • one year ago
  • one year ago

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  1. mathslover
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    @calculusfunctions sir.

    • one year ago
  2. mathslover
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    I had come up with : tan (A+B) = -1

    • one year ago
  3. mathslover
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    so (A+B) = ?

    • one year ago
  4. Coolsector
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    A+B = -45 + 180 * k

    • one year ago
  5. mathslover
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    is it, 7pi /4

    • one year ago
  6. waterineyes
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    \[\tan(A+B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A) \cdot \tan(B)}\]

    • one year ago
  7. Coolsector
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    -45 = pi/4 180 = pi so -pi/4 + pi = 3pi/4 -pi/4 + 2pi = 7pi/4 and so on..

    • one year ago
  8. waterineyes
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    If you calculated it right then: \[A+B= \tan^{-1}(-1)\]

    • one year ago
  9. Coolsector
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    so 7pi/4 is one possibility

    • one year ago
  10. 03453660
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    \[A+B = \tan^{-1}\frac{ -1 }{ 2 }+\tan^{-1} \frac{ -1 }{ 3 }\]

    • one year ago
  11. mathslover
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    so it can be : 3 pi / 4, 7pi/4 , . ... It can not be 5 pi / 4 because it will be positive for tan.

    • one year ago
  12. mathslover
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    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.

    • one year ago
  13. mathslover
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    So it will be 3 pi/4 ? or none?

    • one year ago
  14. hartnn
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    it will be 3pi/4 are any constraints given?

    • one year ago
  15. mathslover
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    constraints?

    • one year ago
  16. hartnn
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    like A+B should be between 0 to 90 or something like this ?

    • one year ago
  17. hartnn
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    else 3pi/4 is correct

    • one year ago
  18. mathslover
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    ok thanks a lot @hartnn :)

    • one year ago
  19. sara12345
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    wud tan(A+B) formula work for all angles

    • one year ago
  20. hartnn
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    yes.

    • one year ago
  21. sara12345
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    ok thank you :D

    • one year ago
  22. waterineyes
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    \[\pi - \frac{\pi}{4} = \frac{3 \pi}{4}\]

    • one year ago
  23. waterineyes
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    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 : \[\tan^{-1}(-x) = \pi - \tan^{-1}(x)\]

    • one year ago
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