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For all values x for which the terms are defined, fidnteh value(s) of k, 0<k<1, such that

cot(x/4) - cot(x) = [sin(kx)]/[sin(x/4)sin(x)]


  • Math -

    That is a very confusing question, you may want to reword that if you want an answer

  • Math -

    the left side
    = cot(x/4) - cot(x)
    = [cos(x/4)/sin(x/4)] - cos(x)/sin(x)
    = [sin(x)cos(x/4)- cos(x)sin(x/4)]/[sin(x/4)sin(x)]
    = sin(x - x/4)/[sin(x/4)sin(x)]

    comparing left side with right side, we notice the denominators are the same, so the numerator has to be the same

    then sin(x - x/4) = sin (kx)
    and x-x/4 = kx
    3x/4 = kx
    k = 3/4

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