Ideas required to solve the problem:

The general solution of any trigonometric equation is given as –

• sin x = sin y, implies x = nπ + (– 1)ⁿy, where n ∈ Z.

• cos x = cos y, implies x = 2nπ ± y, where n ∈ Z.

• tan x = tan y, implies x = nπ + y, where n ∈ Z.

Given,

We know that, cos 150° =

∴

If cos x = cos y then x = 2nπ ± y, where n ∈ Z.

For above equation y = 5π / 6

∴ x = 2nπ ± 5π / 6 ,where n ϵ Z

Thus, x gives the required general solution for the given trigonometric equation.