доказать тождество : sin 9x + sin 10x + sin 11x + sin 12 x = 4 cos x/2 cosx sin 21/2

(sin9x + sin12x) + (sin10x+sin12x) = 4 cos x/2 cosx sin 21/2

2sin (9x+12x) / 2 * cos (9x-12x) / 2 + 2sin (10x+11x) / 2 * cos (10x-11x) / 2=4 cos x/2 cosx sin 21/2

2sin2121x/2 * cos3x/2+sin21x/2 * cosx/2 = 4 cos x/2 cosx sin 21/2

2sin21x/2 (cos3x/2 + cosx/2) = 4 cos x/2 cosx sin 21/2

2sin21x/2 * 2 (cos3x/2 + x/2) / 2 * cos (3x/2 - x/2) / 2 = 4 cos x/2 cosx sin 21/2

4sin21x/2 * 2cosx * cos x/2 = 4 cos x/2 cosx sin 21/2