Question

Solve on the interval 0 2pi. 2sec(x)+6=2

Answer 1

x =
`(2\pi )/(3)`, x =
`(4\pi )/(3)`

Explanation:

using the trigonometric identity

• sec x =
`(1)/(cosx)`

isolate sec x by subtracting 6 from both sides and dividing both sides by 2

2sec x = - 4 ⇒ sec x = - 2, hence

`(1)/(cosx)` = - 2

⇔ cosx = -
`(1)/(2)`

since cos x < 0 then x is in second/ third quadrant

x =
`(2\pi )/(3)` or x =
`(4\pi )/(3)`