Sinx+sin2x+sin3x=cosx+cos2x+cos3x доказать тождество

sin (x)+sin (2x)+sin (3x)=cos (x)+cos (2x)+cos (3x) sin (2x)+sin (2x – x)+sin (2x+x)=cos (2x)+cos (2x – x)+cos (2x+x) sin (2x)+sin (2x) ·cos (x) – cos (2x) ·sin (x)+sin (2x) ·cos (x)+cos (2x) ·sin (x)=cos (2x)+cos (2x) ·cos (x)+sin (2x) ·sin (x)+cos (2x) ·cos (x) – sin (2x) ·sin (x) sin (2x)+2·sin (2x) ·cos (x)=cos (2x)+2·cos (2x) ·cos (x) sin (2x) ·[1+2·cos (x) ]=cos (2x) ·[1+2·cos (x) ] [sin (2x) – cos (2x) ]·[1+2·cos (x) ]=0 1) sin (2x) – cos (2x)=0 sin (2x)=cos (2x) tg (2x)=1 2x=π/4+π·n=π (4n+1) /4 x=π (4n+1) /8 2) 1+2·cos (x)=0 cos (x)=–½ x=±2π/3+2·π·n=2π (3n ± 1) /3 Ответ: {x=π (4n+1) /8 {x=2π (3n ± 1) /3 n — целое.