На "4". Решите уравнение:

1) cos2x-9cosx+8=0

2) 3cosx+sinx=0

3) 3sin2x+sinxcosx - 2cos2x=0

1) cos2x - 9cosx + 8 = 0

2cos²x - 1 - 9cosx + 8 = 0

2cos²x - 9cosx + 7 = 0

D = 81 - 4*2*7 = 25

cosx = t, I t I ≤ 1

2t² - 9t + 7 = 0

t₁ = (9 - 5) / 4

t₁ = 1

t₂ = (9 + 5) / 4

t₂ = 7/2 не удовлетворяет условию I t I ≤ 1

cosx = 1

x = 2πk, k∈Z

2) 3cosx + sinx = 0 делим на cosx ≠ 0

3 + tgx = 0

tgx = - 3

x = - arctg (3) + πn, n∈Z

3) 3sin2x + sinxcosx - 2cos2x = 0

3sin2x + 1/2sin2x - 2cos2x = 0

3,5 * sin2x - 2cos2x = 0 делим на cos2x ≠ 0

3,5tg2x - 2 = 0

tg2x = 4/7

2x = arctg (4/7) + πn, n∈Z

x = (1/2) * arctg (4/7) + πn/2, n∈Z