Вопрос пользователя:
Представьте в виде произведения cos2t-cos4t-cos6t+cos8t
Илюха отвечает:
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*sint