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show that cot inverse (1) + cot inverse (2) + cot inverse (3) = pi/4 ?

  • one year ago
  • one year ago

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  1. SmoothMath
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    I believe this is not actually true...

    • one year ago
  2. SmoothMath
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    cotangent is the ratio of cosine to sine for an angle. Inverse cotangent means that for a specific ratio, the output will be the angle that has that ratio. \(cot^{-1}(1)\) will give us the angle for which cosine is equal to sine. This turns out to be pi/4 Add in \(cot^{-1}(2)\) and \(cot^{-1}(3)\) and clearly the angle won't be pi/4 anymore.

    • one year ago
  3. Coolsector
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    arccot(x) = arctan(1/x) if x>0 so arctan(1) = arccot(1) = pi/4 the rest are positive so it cant be true arccot(2) = arctan(1/2) > 0 arccot(3) = arctan(1/3) > 0

    • one year ago
  4. Coolsector
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    yes looks like we wrote the same thing lol

    • one year ago
  5. SmoothMath
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    Correct =)

    • one year ago
  6. SmoothMath
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    This problem was almost certainly meant to say = pi/2

    • one year ago
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