Решить уравнение:

6sin^2x - 11cosx - 10 = 0

6sin^2x - 11cosx - 10 = 0 sin^2x = (1-cosx^2x),

6 * (1-cosx^2x) - 11cosx - 10 = 0

6 - 6cosx^2x - 11cosx - 10 = 0

6cosx^2x + 11cosx + 4 = 0 замена cosx=а

6 а²+11 а+4=0

D=121 - 96=25 √D=5

a₁ = (-11+5) / 12=-1/2

a₂ = (-11-5) / 12=-16/12 = - 4/3

cos (x) = - 1/2 cos (x) = - 4/3

х = 2π/3+2πn₁ n₁∈Z x = cos⁻¹ (-4/3) + 2πn n∈Z

x=4π/3+2πn₂ n₂∈Z x = 2πn - cos⁻¹ (-4/3) n∈Z