Question

Упростите выражение :
sin (3х + 2у) cos (х+2у) - sin (х+2у) cos ( 3х+2у) = ?
Срочно

Answer 1

sin(3x+2y)cos(x+2y)-sin(x+2y)cos(3x+2y)=
=1/2·[sin(3x+2y+x+2y)+sin(3x+2y-x-2y)]-1/2·[sin(x+2y+3x+2y)+sin(x+2y-3x-2y)]=
=1/2·[sin(4x+4y)+sin(2x)-sin(4x+4y)-sin(-2x)]=
=1/2·(sin2x+sin2x)=sin2x;