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trig

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Help find the general solution to:sin^2x-3cosx+sinxcosx-3sinx=0

  • trig - ,

    sin^2x-3cosx+sinxcosx-3sinx=0
    sin^2x - 3sinx + sinxcosx - 3cosx = 0
    sinx(sinx - 3) + cosx(sinx - 3) = 0
    (sinx - 3)(sinx + cosx) = 0
    sinx = 3 , which is not possible
    or
    sinx = -cosx
    sinx/cosx = -1
    tanx = -1
    x = 135° or 225° or in radians, 3π/4 , 5π/4
    the period of tanx = 180° or π radians

    general solution: = 3π/4 + kπ
    or
    x = 5π/4 + kπ , where k is an integer

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