Соs2t-cos4t-cos6t+cos8t

cos2t - cos4t - cos6t + cos8t = (cos2t + cos8t) - (cos 4t + cos6t) =

= 2cos (2t + 8t) / 2 * cos (2t - 8t) / 2 - 2cos (4t + 6t) / 2 * cos (4t - 6t) / 2 =

= 2cos5t * cos3t - 2cos5t * cost = 2cos5t (cos3t - cost) =

= - 4cos5t * sin (3t + t) / 2 * sin (3t - t) / 2 = - 4cos5t * sin2t * si

или если речь идет не о представлении в виде произведения

Соs2t-cos4t-cos6t+cos8t=cos2t (1-2-3+4) = cos2t