Question

Доказать тождество:
sinx+siny+sin(x-y)=4sin(x/2)cos(x/2)cos((x-y)/2)

Answer 1

sinx+siny+sin(x-y)=4sin(x/2)cos(x/2)cos((x-y)/2);
sinx+siny+sin(x-y)=2sin((x+y)/2)·cos((x-y)/2)+2sin(x-y)/2·cos(x-y)/2=
=2cos((x-y)/2)·[sin(x+y)/2+sin(x-y)/2)]=
=2cos((x-y)/2)·2sin((x+y+x-y)/4)·cos((x+y-x+y)/4)=
=4cos((x-y)/2)·sin(x/2)·cos(y/2)

Answer 2

по формуле:sinx+siny=2sin((x+y)/2)*cos((x-y)/2)

Answer 3

а это 2sin(x-y)/2·cos(x-y)/2 ???

Answer 4

извините :D

Answer 5

все

Answer 6

понял