Question

упростите выражение

 

кос3х-син 4х-кос 5х

Answer 1

cos(3x) - sin(4x) - cos(5x) = [cos(3x) - cos(5x)] - sin(4x) = [-2sin(4x)*sin(-x)] - sin(4x) = 2sin(4x)*sinx - sin(4x) = sin(4x)*(2sinx-1) = 2sin(2x)*cos(2x)*[2sinx - 1] = 2*[2sinx*cosx]*[1-2sin^2(x)]*[2sinx - 1] = [4sinx*cosx - 8sin^3(x)*cosx]*[2sinx - 1] = 8sin^2(x)*cosx - 4sinx*cosx - 16sin^4(x)*cosx + 8*sin^3(x)*cosx