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# how do you solve this trig equation? how do you simplify to isolate x?

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

### 1 Answer by Expert Tutors

Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
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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
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
or x = (7 pi)/4+2 pi
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:

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