Question

Решить уравнение 4sinx*cosx*cos2x*cos8x=sin12x.

Answer 1

2sin2x*cos2x*cos8x=sin12x
sin4x*cos8x=sin12x
1/2(sin12x+sin4x)=sin12x
1/2sin12x+1/2sin4x-sin12x=0
1/2sin4x-1/2sin12x=0
1/2*2sin(-4x)*cos8x=0
-sin4x*cos8x=0
sin4x*cos8x=0
sin4x=0        или   cos8x=0
4x=$pi n$, n-целое        
x=$pi /4$, n-целое
cos8x=0
8x=$pi /2+ pi n$, n - целое
x=$pi /16+ pi n/8$, n - целое

Answer 2

1/2(sin12x+sin(-4x)=sin12x
1/2sin12x-1/2sin4x-sin12x=0
-1/2sin4x-1/2sin12x=0