Question

sin2x+sinx+sin4x+sin5x
упростить

Answer 1

$Sin2x+Sinx+Sin4x+Sin5x=(Sin2x+Sin4x)+(Sinx+Sin5x)=\\\\=2Sin\frac{2x+4x}{2}Cos\frac{2x-4x}{2}+2Sin\frac{x+5x}{2}Cos\frac{x-5x}{2} =2Sin3xCosx+2Sin3xCos2x=\\\\=2Sin3x(Cosx+Cos2x)=2Sin3x*2Cos\frac{x+2x}{2}Cos\frac{x-2x}{2}=\\\\=4Sin3xCos\frac{3x}{2}Cos\frac{x}{2}$