Представьте в виде произведения cos2t-cos4t-cos6t+cos8t - вопрос №246883492 от jajahahah81817 02.05.2022 18:28

Question

Математика: Представьте в виде произведения cos2t-cos4t-cos6t+cos8t

jajahahah81817 · Answer

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