а) 3 tg^3 x - 2 tg x - 1=0tgx = t3t³ - 2t - 1 = 0t₁ = 1 3t³ - 2t - 1 I
t - 1-
(3t³ - 3t²
) 3t² + 3t + 1 3t² - 2t
-(3t²
- 3t) t - 1 -
(t - 1) 0 3t³ - 2t - 1 = (t - 1)*(3t² + 3t + 1)3t² + 3t + 1 = 0D = 9 - 4*3*1 = - 3 < 0 решений нетtgx = 1x = π/4 + πk, k∈Zb) ctg^3 2x - 6 ctg 2x + 5= 0ctg2x = yy³ - 6y + 5 = 0y = 1 y³ - 6y + 5
I y - 1-
(y³ - y²) y² + y - 5 y² - 6y -(
y² - y) - 5y + 5 -
(-5y + 5) 0y³ - 6y + 5 = (y - 1)*(y² + y - 5)ctg2x = 12x = π/4 + πn, n∈Zx₁ = π/8 + πn/2, n∈Zy² + y - 5 = 0D = 1 + 4*1*5 = 21y₁ = (- 1 - √21)/2y₂ = (- 1 + √21)/2ctg2x = (- 1 - √21)/22x = arctg (- 1 - √21)/2) + πm, m∈Zx₂ = 1/2 arctg (- 1 - √21)/2) + πm/2, m∈Zctg2x = (- 1 + √21)/22x = arctg (- 1 + √21)/2) + πm, m∈Zx₃ = 1/2 arctg (- 1 + √21)/2) + πm/2, m∈Z