Solve for all exact solutions

Solve for all exact solutions. Write answers using least non-negative angle measures.

2(sqrt3) cos (x/2) = -3

2√3 cos(1/2) = -3

You first need to divide 2√3 to both sides.
cos(1/2)=-3/2√3

Then you need to rationalize the expression (so that no square root sign is in the denominator)
-3/2√3= -3√3/6

Simplify
-√3/2

cos(1/2)=-√3/2
The cosign of 1/2 is equal to -√3/2 in the 2nd and 4th quadrants.

Now, because the answers are in the 2nd and 4th quadrants and the reference angle is 60 degrees, you are looking at the angles of 120 and 300.

120= 5π/3
300=7π/3

Please rate for best answer if my walk through helped :)

2√3 * cos(x/2) = -3 The rule is you can do any valid operation to both sides of an equation and it will still be equal. So divide by 2√3.

cos(x/2) = -3/(2√3) Multiply by √3/√3.

cos(x/2) = -3√3/(2 * 3)

cos(x/2) = -(√3)/2

Remember Chief SohCahToa
Sin = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Also memorize:
Sec = 1/Cos
Csc = 1/Sin
Cot = 1/Tan

x/2 is in the second quadrant, 150° so x = 300°.

2(sqrt3)cos(x/2)=-3

Step 1: cos(x/2)=-3/2(sqrt3)
=>cos(x/2)=-sqrt3/2

Step 2: x/2)= cos'1[-sqrt3/2]

=>x/2=150

=>x=300
Thats it...,

Cos(x/2)=-(sqrt3)/2
Cos is that value at 5pi/6 and 7pi/6.
Thus the two results are 5pi/3 and 7pi/3