sin2x+sin3x+sin4x+sin5x=0 [П; 2 П]

Sin2x+sin3x+sin4x+sin5x = 2 sin3x * cosx + 2 sin4x * cosx = 2cosx * (sin3x + sin4x) =

= 4cosx sin (7x/2) cos (x/2)

4cosx sin (7x/2) cos (x/2) = 0

cos x = 0 или sin (7x/2) = 0 или cos x/2 = 0

x = 3 П/2 x = 8 П/7 x = П

х=10 П/7

х=12 П/7

х=2 П