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A maths! Trigonometric questions!

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  • bonkysleuth
    bonkysleuth's Avatar
    314 posts since Mar '07
    • 07 Sep `08, 6:39PM

      Need help with this question. Here goes:

       

      Find the values of x, where 0 deg < x < 180 deg, such that

      8 cosec 2x cot 2x = 3

       

      Thanks guys!

  • Moderator
    eagle
    eagle's Avatar
    17,968 posts since Aug '01
    • 07 Sep `08, 7:04PM

      cot 2x = cos 2x * cosec 2x

      hence, 8 cosec 2x cos 2x cosec 2x = 3

      8 cos 2x = 3 (sin 2x )^2
      8 cos 2x = 3 - 3 (cos 2x )^2
      3 (cos 2x )^2 + 8 cos 2x - 3 = 0
      (3 cos 2x -1) (cos 2x + 3) = 0
      cos 2x = 1/3  or  cos 2x = -3 (reject because cos is between -1 and 1)

      0 deg < x < 180 deg
      0 deg < 2x < 360 deg

      so 2x = 70.53, 298.47
      x = 35.3 deg, 144.7 deg

      Regards,
      Eagle (Strategic Tuition)

      Edited by eagle 07 Sep `08, 7:04PM
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