Math
posted by Gina .
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)]
PLEASEEEE HELP! ASAP!

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

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 xx/4 = kx
3x/4 = kx
k = 3/4