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Math Help - Is tan(x + 90) = -cot(x)?

  1. #1
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    Is tan(x + 90) = -cot(x)?

    Is tan(x + 90) = -cot(x) ?
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  2. #2
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    Re: Is tan(x + 90) = -cot(x)?

    Yes, tan(x+ 90)= \frac{sin(x+ 90)}{cos(x+ 90)}= \frac{cos(x)}{-sin(x)}= -cot(x). (I am assuming that your "x" and "90" are in degrees since that is the only way this would be true.)
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  3. #3
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    Re: Is tan(x + 90) = -cot(x)?

    By \tan(x+90), I assume you mean \tan(x+90^\circ). Use the sum of angles formulas for sine and cosine.

    \tan(x+90^\circ) = \dfrac{\sin(x+90^\circ)}{\cos(x+90^\circ)}
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  4. #4
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    Re: Is tan(x + 90) = -cot(x)?

     tan(x+90) = -cot(x)

    \frac{tan(x) + tan(90)}{1-tan(x)tan(90)} = -\frac{1}{tan(x)}

     tan^2(x) + tan(x)tan(90) = tan(x)tan(90) - 1

     tan(x) = \sqrt{-1}

    Then what did I do wrong?
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  5. #5
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    Re: Is tan(x + 90) = -cot(x)?

    \tan(90^\circ) is not defined. That is why you were told to use the sum of angles formulas for sine and cosine, not the sum of angles formula for tangent.
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