Объяснение:
a) 2cos²x - cosx-1 = 0
cosx = y
2y²-y-1 = 0
D = 1+8 = 9
y ₁ ₂ = (1±3)/4
y₁ = 1
y₂ = -1/2
cosx = 1
x = 2πn n∈Z
cosx = -1/2
x = 2π/3 + 2πn
x = 4π/3 + 2πn
n∈Z
б) 3sin²x+sinx*cosx-2cos²x = 0
разделим все на cos²x
3tg²x+tgx-2 = 0
tgx = y
3y²+y-2 = 0
D = 1+24 = 5²
sinx ≥√3/2
x∈ [π/3 + 2πn; 2π/3+2πn]
y ₁ ₂ = (-1 ±5)/6
y₁ = -1
y₂ = 2/3
tgx = 1 x = -π/4 + πn
tgx = 2/3
x = arctg(2/3) + πn
в) аналогично делим на cos x
3tgx = 2
cosx <-
x∈ (5π/6 + 2πn; 7π/6 + 2πn)
Объяснение:
a) 2cos²x - cosx-1 = 0
cosx = y
2y²-y-1 = 0
D = 1+8 = 9
y ₁ ₂ = (1±3)/4
y₁ = 1
y₂ = -1/2
cosx = 1
x = 2πn n∈Z
cosx = -1/2
x = 2π/3 + 2πn
x = 4π/3 + 2πn
n∈Z
б) 3sin²x+sinx*cosx-2cos²x = 0
разделим все на cos²x
3tg²x+tgx-2 = 0
tgx = y
3y²+y-2 = 0
D = 1+24 = 5²
sinx ≥√3/2
x∈ [π/3 + 2πn; 2π/3+2πn]
y ₁ ₂ = (-1 ±5)/6
y₁ = -1
y₂ = 2/3
tgx = 1 x = -π/4 + πn
tgx = 2/3
x = arctg(2/3) + πn
в) аналогично делим на cos x
3tgx = 2
tgx = 2/3
x = arctg(2/3) + πn
cosx <-
x∈ (5π/6 + 2πn; 7π/6 + 2πn)