Question

Упрастите пожалуйста 4cos(a+П/3)cos(a+2П/3)cosa+cos3a.

Answer 1

4*1/2*[cos(a+π/3-a-2π/3)+cos(a+π/3+a+2π/3)]*cosa+cos3a=
=2(cos(-π/3)+cos(2a+π))*cosa+cos3a=2(1/2-cos2a)*cosa+cos3a=
=(1-2cos2a)*cosa+cos3a=cosa+cos3a-2cos2a*cosa=
=2cos2acosa-2cos2acosa=0