Question 371826
cos t+cos4t+cos7t = -2cos4tcos3t + cos4t = cos4t(1-2cos3t), by using {{{-2cos((A+B)/2)cos((A-B)/2) = cosA + cosB}}}.
Similarly,
sin t+sin4t+sin7t = -2sin4tcos3t + sin4t = sin4t(1-2cos3t), using {{{2sin((A+B)/2)cos((A-B)/2) = sinA + sinB}}}.  Therefore
 {{{(cos t+cos4t+cos7t) / (sin t+sin4t+sin7t)= (cos4t(1-2cos3t))/(sin4t(1-2cos3t)) = cot4t}}}.