Решите уравнение 6sin^2x=5sinxcosx-cos^2x

Решение

6sin^2x=5sinxcosx-cos^2x

6sin^2x - 5sinxcosx + cos^2x = 0 делим на ²x ≠ 0

6tg ²x - 5tgx + 1 = 0

tgx = t

6t ² - 5t + 1 = 0

D = 25 - 4*6*1 = 1

t = (5-1) / 12

t = 1/3

t = (5+1) / 12

t = 1/2

1) tgx = 1/3

x ₁ = arctg (1/3) + πk, k ∈ Z

2) tgx = 1/2

x ₂ = arctg (1/2) + πn, n ∈Z