How to find all solutions of equation (2*cosx-square root3)(11sinx-9)=0?

We'll start from the fact that a product is zero if one of
it's factors is zero.

We'll set the first factor as
zero.

2*cosx-sqrt3 = 0

We'll
add sqrt3 both sides:

2cos x =
sqrt3

cos x = sqrt3/2

x =
+/-arccos(sqrt3/2) + 2kpi, k is an integer number

x =
+/-(pi/6) + 2kpi

Let's put the next factor equal to
zero.

11sinx-9 = 0

We'll add 9
both sides:

11sin x = 9

We'll
divide by 11:

sin x = 9/11

x =
(-1)^k*arcsin(9/11) + k*pi

The solutions of
the equation are: {+/-(pi/6) + 2kpi} U {(-1)^k*arcsin(9/11) +
k*pi}.