Question

cos3x+cos2x+cosx=0 решить уравнение

Answer 1

cos2x+(cosx+cos3x)=cos2x+(2cos (3x+x)/2*cos(3x-x)/2)=cos2x+2cos2xcosx=cos2x(1+2cosx)=0
cos2x=0
2x=+-p/2+2pk
x=+-p/4+pk

1+2cosx=0
cosx=-1/2
x=+-p/6+2pk