Question

Представив 3х в в виде х+2х,докажите тождество сos3x=4cos^3x-3cosx

Answer 1

cos 3x = cos (x+2x) =cos (x) *cos (2x) - sin(x) *sin (2x)=cos(x) * (cos^2 (x) - sin^2 (x) ) - 2 * sin (x) *sin(x) * cos(x)=cos(x) * (2*cos^2 (x) - 1 ) - 2 * (1-cos^2(x) * cos(x)= 2 cos^3 (x) - cos (x) - 2 *cos(x) + 2* cos^3(x) = 4* cos^3 (x) - 3* cos(x)