Упростите выражение 1) sinx+sin2x+sin3x+sin4x

2) cos2y-cos4y-cos6y-cos8y

3) 1-cos2a/sin (П+2 а) (tg П/2 + а)

4) cos (3 П/2 - 2 а) / 1+cos2a ctg (П+а)

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