# Solve for x: 2(cos x) ^2 - sqrt 3 *cos x = 0 for 0 degree < x < 360 degree.

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Expert Answers

justaguide | Certified Educator

We have 2(cos x) ^2 - sqrt 3 *cos x = 0

=> cos x (cos x – sqrt 3) = 0

For cos x – sqrt 3 = 0, we have cos x = sqrt 3

Therefore cos x is 0 and sqrt 3

x = arc cos 0 and arc cos (sqrt 3).

Now arc cos 0 = 90 degrees and 270 degrees in the given range for x.

arc cos (sqrt 3) = 30 degrees and 330 degrees in the given range.

**Therefore x is equal to 90, 270, 30 and 330 degrees.**

Student Comments

neela | Student

To solve for x: 2(cos x) ^2 - sqrt 3 *cos x = 0 for 0 degree < x < 360 deg.

We factor the given equation and write:

cosx(2cosx - sqrt3) = 0.

So cosx = 0. Or 2xosx - sqrt3) = 0.

cosx = 0, or** x = pi/2 rad = 90 deg. **

**Or x= 3pi/2 rad = 270 deg**

OR ( 2cosx - (sqrt3)/2) = 0.

cosx = (sqrt3)/2. x = pi/6 radians = **30 degree. **

x = 2pi-pi/6 = 11pi/6 radians = **330 degrees.**