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Math Help - trigo equation problem

  1. #1
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    trigo equation problem

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  2. #2
    MHF Contributor
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    Why not expand it then?

    (1 +sinX)(tanX -cotX) +2cosX = 0
    tanX -cotX +sinXtanX -sinXcotX +2cosX = 0
    tanX -cotX +sinX[sinX/cosX] -sinX[cosX/sinX] +2cosX = 0
    tanX -cotX +[sin^2(X)/cosX] -cosX +2cosX = 0
    tanX -cotX +[(1 -cos^2(X)) /cosX] +cosX = 0
    tanX -cotX +[1/cosX -cosX] +cosX = 0
    tanX -cotX +1/cosX = 0

    sinX/cosX -cosX/sinX +1/cosX = 0

    Clear the fractions, multiply both sides by sinXcosX,
    sin^2(X) -cos^2(X) +sinX = 0

    sin^2(X) -[1 -sin^2(X)] +sinX = 0
    2sin^2(X) +sinX -1 = 0

    (2sinX -1)(sinX +1) = 0

    2sinX -1 = 0
    sinX = 1/2
    X = 30deg, 150deg

    sinX +1 = 0
    sinX = -1
    X = 270 deg

    The 30 and 150 degrees check with the original equation, but the 270 degress did not.

    Therefore, in the interval 0 <= X <= 360deg,
    X = 30 deg or 150 deg -------------------------answer.
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