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Truth set of x ?

Find the truth set given that sinx° = sin2x if 0<=x°<=360°

2 Answers

Relevance
  • 2 months ago

    sin2x = 2sinxcosx

    so, sinx = 2sinxcosx

    i.e. 2sinxcosx - sinx = 0

    or, sinx(2cosx - 1) = 0

    Hence, sinx = 0 or cosx = 1/2

    Then, x = 360n°, 180 + 360n°, 60° + 360n° or -60 + 360n°...for n = 0, 1, 2,...

    so, x = 0°, 60°, 180° and 300°...for 0° ≤ x ≤ 360°

    Note: I've never heard of the 'truth' or 'false' set before!!

    :)>

  • atsuo
    Lv 6
    2 months ago

    One method :

    sin(x) = sin(2x)

    sin(x) = sin(x+x)

    sin(x) = 2sin(x)cos(x)

    sin(x)(1 - 2cos(x)) = 0

    case1. sin(x) = 0 

    x = 0° or 180° or 360°

    case2. cos(x) = 1/2 

    x = 60° or 300°

    Another method:

    sin(x) = sin(2x)

    case1. x + 360n = 2x (n:integer) 

    -x = -360n

    x = 360n so x = 0° or 360°

    case2. x + 360n = 180 - 2x (n:integer) 

    3x = 180 - 360n

    x = 60 - 120n so x = 60° or 180° or 300°

    The truth set is {0°,60°,180°,300°,360°}

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