представить в виде произведения cos 2t - cos 4t - cos 6t + cos 8t

Question

представить в виде произведения

cos 2t - cos 4t - cos 6t + cos 8t

Answer 1

cos2t+cos8t=2cos5tcos3t

cos4t+cos6t=2cos5tcost

=2cos5t(cos3t-cost)=-4cos5tsin2tsint

Answer 2

(cos 2t +cos8t) - (cos 4t + cos 6t) = 2cos[(2t+8t)/2]cos[(2t-8t)/2] - 2cos[(4t+6t)/2]cos[(4t-6t)/2] = 

= 2cos5tcos3t - 2cos5tcost = 2cos5t(cos3t - cost)