Sin3x-sin5x=0 2sin2x+5sinx=0 sin2x+4cos²x=0

1)sin3x-sin5x=0 2*sin (3x-5x)/2 * cos (3x+5x)/2 = 0sinx = 0 x = πk, k є Z илиcos4x = 04x = π/2+ πk, k є Z x = π/8+ πk/4, k є Z.2)2sin2x+5sinx=02*2sinx*cosx + 5sinx = 0sinx*(4cosx + 5) = 0sinx = 0x = πk, k є Zили4cosx + 5 = 04cosx = -5cosx = -5/4косинус лежит в пределах от -1 до+1x є Ø3)sin2x+4cos²x=02sinx*cosx + 4cos²x=02cosx*(sinx + 2cosx) = 0cosx = 0x = π/2+ πk, k є Zилиsinx + 2cosx = 0 |:cosxtgx + 2 = 0tgx = -2x= arctg(-2) + πk, k є Zx= -arctg2 + πk, k є Z