4cos^2x - 3sinx - 3 = 0
4(1 - sin^2x) - 3sinx - 3 = 0
4 - 4sin^2x - 3sinx - 3 = 0
- 4sin^2x - 3sinx + 1 = 0 // : (-1)
4sin^2x + 3sinx - 1 = 0
Пусть sinx = t , тогда :
4t^2 + 3t - 1 = 0
Δ = 9 + 16 = 25
t1 = ( - 3 +5)/8 = 1/4
t2 = ( - 3 - 5)/8 = - 1
sinx = 1/4
x = (-1)^k arcsin(1/4) + pik, k ∈ Z
sinx = 1
x = -π/2 + 2πn, n ∈ Z.
4cos^2x - 3sinx - 3 = 0
4(1 - sin^2x) - 3sinx - 3 = 0
4 - 4sin^2x - 3sinx - 3 = 0
- 4sin^2x - 3sinx + 1 = 0 // : (-1)
4sin^2x + 3sinx - 1 = 0
Пусть sinx = t , тогда :
4t^2 + 3t - 1 = 0
Δ = 9 + 16 = 25
t1 = ( - 3 +5)/8 = 1/4
t2 = ( - 3 - 5)/8 = - 1
sinx = 1/4
x = (-1)^k arcsin(1/4) + pik, k ∈ Z
sinx = 1
x = -π/2 + 2πn, n ∈ Z.