Solve on the interval : [0,2pi]

4 csc x +6=-2

a. 7pi/6 , 11pi/6

b. pi/6 , 5pi/6

c. pi/3 , 5pi/3

d. 2pi/3 , 4pi/3

A. x = 0, x = -3, x = 2, and x = -2

Step-by-step explanation:

by moving the terms on the left side to the right side

factor an from

and factor - 4 from

the equation becomes :

= 0

take  as  a common factor the equation becomes :

= 0

thus

⇒

and

by factoring an x we get :

⇒ = 0 and

⇒ and

Thus

the values are :

x = 0, x = -3, x = 2, and x = -2