Question

If cos^2 x + √3 cos x - 3=0
cos x =?​

Answer 1

Answer:

Changing sin

2

x into 1−cos

2

x; we get

2(1−cos

2

x)+

3

cosx+1=0

or 2cos

2

x−

3

cosx−3=0

∴cosx=

4

3

±

3+24

=

4

3

+3

3

=

3

or

2

−

3

Since

3

is greater than 1 it is not admissible as cosx can not be greater than 1.

∴cosx=−

3

/2=−cos(π/6)

=cos(π−π/6)=cos(5π/6)

∴x=2nπ±(5π/6)