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Math Help - solve x for tan and cot

  1. #1
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    solve x for tan and cot

    Please help me to solve x:

    tan (3x - 10) = cot (x + 10) , 0 <= x <= 90, (in degrees)
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  2. #2
    Member Glaysher's Avatar
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    Quote Originally Posted by Nico View Post
    Please help me to solve x:

    tan (3x - 10) = cot (x + 10) , 0 <= x <= 90, (in degrees)
    sin (3x - 10)/cos (3x - 10) = cos (x + 10)/sin (x + 10)

    sin (3x - 10) sin (x +10) = cos (3x - 10) cos (x + 10)

    0 = cos (3x - 10) cos (x + 10) - sin (3x - 10) sin (x +10)

    0 = cos (3x - 10 + x + 10)

    0 = cos 4x

    4x = 90, 270

    x = 22.5, 67.5
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  3. #3
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    Quote Originally Posted by Nico View Post
    Please help me to solve x:

    tan (3x - 10) = cot (x + 10) , 0 <= x <= 90, (in degrees)
    Here is an easy way to get one of the solutions.

    Since tangent and cotangent are cofunctions. It means that they differ by 90 degrees.

    Thus the angle sum between the tangent and cotangent should be 90 degrees.

    3x-10+x+10=90

    4x=90

    x=22.5
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