представить в виде произведения
cos 2t - cos 4t - cos 6t + cos 8t
cos2t+cos8t=2cos5tcos3t
cos4t+cos6t=2cos5tcost
=2cos5t(cos3t-cost)=-4cos5tsin2tsint
(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)
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Answers & Comments
cos2t+cos8t=2cos5tcos3t
cos4t+cos6t=2cos5tcost
=2cos5t(cos3t-cost)=-4cos5tsin2tsint
Verified answer
(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)