# Math

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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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