1) 3SinxCosx - 2Cos²x = 0
Cosx(3Sinx - 2Cosx) = 0
или Cosx = 0 или 3Sinx - 2Cosx = 0
x = π/2 + πn, n ∈ z 3Sinx/Cosx - 2Cosx/Cosx=0 Cosx≠0
3tgx - 2 = 0
tgx = 2/3
x = arctg2/3 + πn, n ∈ z
2) 7Sin²x = 8SinxCosx - Cos²x
7Sin²x - 8 SinxCosx + Cos²x = 0
7Sin²x/Cos²x - 8SinxCosx/Cos²x + Cos²x/Cos²x = 0 Cosx ≠ 0
7tg²x - 8tgx + 1= 0
tgx = m
7m² - 8m + 1 = 0
D/4 = 4² - 1*7 = 16 - 7= 9
m₁,₂ = (4 + - √9)/7 = (4 + - 3)/7
m₁ = (4+3)/7 = 1
m₂ = (4-3)/7 = 1/7
tgx₁ = 1 tgx₂ = 1/7
x₁ = arctg1 +π n,n ∈ z x₂ = arctg1/7 + πn, n ∈ z
x₁ = π/4 + πn,n ∈ z