Szögfüggvény, négy feladatot megoldanátok?

6tg²x = 2

tg²x = 2/6 = 1/3

tgx = 1/√3 = √3/3 = tg30

x = 30 + k*180 (k ∈ Z)

x = 1/6π + kπ (k ∈ Z)

cosx = -1/2

x₁ = 120 + k*360 (k ∈ Z)

x₁ = ⅔π + k*2π (k ∈ Z)

x₂ = 240 + n*360 (n ∈ Z)

x₂ = 4/3π + n*2π (n ∈ Z)

sinx = 2tgx

sinx = 2sinx/cosx

sinxcosx = 2sinx

2sinx - sinxcosx = 0

sinx(2-cosx) = 0

I. sinx = 0

x₁ = k*180 (k ∈ Z)

x₁ = kπ (k ∈ Z)

II. 2-cosx

cosx = 2

Nincs megoldás, mert -1≤cosx≤1.

cos²x + 4cosx = 3sin²x

cos²x + 4cosx = 3(1-cos²x)

cos²x + 4cosx = 3-3cos²x

4cos²x + 4cosx - 3 = 0

cosx₁ = 1/2

cosx₂ = -3/2 (Nem megoldás, mert -1≤cosx≤1)

cosx = 1/2

x₁ = 60 + k*360

x₁ = 1/3π + k*2π (k ∈ Z)

x₂ = 300 +n*360

x₂ = 5/3π + n*2π (n ∈ Z)