1) sinx+sin2x+sin3x+sin4x=0 2) cosx+cos2x+cos3x+cos4x=0

1) sinx+sin2x+sin3x+sin4x=(sinx+sin3x)+(sin2x+sin4x)=2sin2x× cosx+2sin3x× cosx=2cosx (sin2x+sin3x)=4sin (5x/2) × cos (x/2) × cosx sin (5x/2)=0 5x/2=p n x=2p n/5cos (x/2)=0 => x/2=p /2+p n э Z => x=p+2p ncosx=0 x=p /2+p n x=p /2+p n 2p n/5; p (1+2n); p (1/2+n) , n э Z. 2) cosx+cos2x+cos3x+cos4x=02cos (5/2) x*cos (x/2)*2*cos (5/2) x*cos (3/2) x=0cos (5/2) x (cos (x/2)+cos (3/2) x)=02cos (5/2) x*cosx*cos (x/2)=0 cos (5/2) x=0x=p/2+2/5 np, n э Zcosx=0x=p/2+ap, a э Zcos (x/2)=0x=p+2bp, b э zвроде так)