Solve the equation sinx*cos150=0,5-cosx*sin150 if 0

We'll shift the product -cos x*sin 150 to the left
side:

sin x*cos 150 + cos x*sin 150 =
0.5

We'll recognize the
formula:

sin(x+150) = 0.5

But
sin(x+150) = cos (90 - x - 150) = cos (-x - 60)

sin(x+150)
= - cos (x + 60)

We'll re-write the
equation:

- cos (x + 60) =
1/2

x + 60 = arccos (-1/2)

x +
60 = 120

x =
60

or

x + 60 =
240

x = 240 - 60

x =
180

The solutions of the equation, located in
the range (0,360) are: x = 60 degrees = pi/3 radians and x = 180 degrees = pi
radians.