cos x(2sinx + sqr root 3)(-sqr root 2 cosx + 1) = 0

You have 3 terms multiplied together equal to zero.

SO one or more of the terms Must be zero.

cos(x) = 0

or 1-sqrt(2) cos(x) = 0

or sqrt(3)+2 sin(x) = 0

Look at the first equation:

cos(x) = 0

Eliminate the cosine from the left hand side.

Take the inverse cosine of both sides:

x = pi/2+pi

or 1-sqrt(2) cos(x) = 0

Take the inverse cosine of both sides:

x = pi/2+pi

or 1-sqrt(2) cos(x) = 0

or sqrt(3)+2 sin(x) = 0

Look at the second equation:

1-sqrt(2) cos(x) = 0

Isolate terms with x to the left hand side.

Subtract 1 from both sides:

x = pi/2+pi

or -(sqrt(2) cos(x)) = -1 or sqrt(3)+2 sin(x) = 0

Divide both sides by a constant to simplify the equation.

Divide both sides by -sqrt(2):

x = pi/2+pi n_1 for n_1 element Z

or cos(x) = 1/sqrt(2) or sqrt(3)+2 sin(x) = 0

Eliminate the cosine from the left hand side.

Take the inverse cosine of both sides:

x = pi/2+pi

or x = pi/4+2 pi

Subtract 1 from both sides:

x = pi/2+pi

or -(sqrt(2) cos(x)) = -1 or sqrt(3)+2 sin(x) = 0

Divide both sides by a constant to simplify the equation.

Divide both sides by -sqrt(2):

x = pi/2+pi n_1 for n_1 element Z

or cos(x) = 1/sqrt(2) or sqrt(3)+2 sin(x) = 0

Eliminate the cosine from the left hand side.

Take the inverse cosine of both sides:

x = pi/2+pi

or x = pi/4+2 pi

or x = (7 pi)/4+2 pi

or sqrt(3)+2 sin(x) = 0

or sqrt(3)+2 sin(x) = 0

Look at the fourth equation:

sqrt(3)+2 sin(x) = 0

Isolate terms with x to the left hand side.

Subtract sqrt(3) from both sides:

x = pi/2+pi

or x = pi/4+2

or x = (7 pi)/4+2

or 2 sin(x) = -sqrt(3)

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

x = pi/2+pi n_1

or x = pi/4+2 pi

or x = (7 pi)/4+2 pi

or sin(x) = -sqrt(3)/2

Eliminate the sine from the left hand side.

Take the inverse sine of both sides:

Subtract sqrt(3) from both sides:

x = pi/2+pi

or x = pi/4+2

or x = (7 pi)/4+2

or 2 sin(x) = -sqrt(3)

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

x = pi/2+pi n_1

or x = pi/4+2 pi

or x = (7 pi)/4+2 pi

or sin(x) = -sqrt(3)/2

Eliminate the sine from the left hand side.

Take the inverse sine of both sides:

x = pi/2+pi

or x = pi/4+2

or x = (7 pi)/4+2 pi

or x = (4 pi)/3+2 pi

or x = (5 pi)/3+2 pi