Question

Упростите выражение 1)sinx+sin2x+sin3x+sin4x
2)cos2y-cos4y-cos6y-cos8y
3)1-cos2a/sin (П+2а) (tg П/2 +а)
4)cos (3П/2 -2а)/ 1+cos2a ctg(П+а)

Answer 1

1
2sin(5x/2)cos(3x/2)+2sin(5x/2)cos(x/2)=2sin(5x)/2*(cos(3x/2)+cos(x/2))=
=2sin(5x/2)*2cos(x)8cos(x/2)=4sin(5x/2)*cos(x)*cos(x/2)
2
-2sin(-3y)*sin5y-2cos(y/2)*cos5y=2(sin5y*sin3y+cos(y/2)*cos5y)
3

1-cos2a/(-sin2a)*(-ctga)=1-ctg2a*tga=1-tga/tg2a=1-tga*(1-tg²a)/(2tga)=
=1-(1-tg²a)/2=(2-1+tg²a)/2=(1+tg²a)/2=1/2cos²a
3
-sin2a/(1+cos2a) *ctga=[-2sina*cosa/(2cos²a)]*cosa/sina=-2