Question

How do you solve `3 csc^2 x - 2 = 2`?

Answer 1

`+- pi/6 + 2kpi`
`+- (5pi)/6 + 2kpi`

Explanation:

Replace in the equation sec x by `(1/(cos x))`
`3/(cos^2 x) - 2 - 2 = 0`
`(3 - 4cos^2 x)/(cos^2 x) = 0`
(Condition cos x different to zero)
`3 - 4cos^2 x = 0`
`cos^2 x = 3/4`
`cos x = +- sqrt3/2`
a. `cos x = sqrt3/2 --> x = +- pi/6`
b. `x = -sqrt3/2 --> x = +- (5pi)/6`
General answers:
`x = +- pi/6 + 2kpi`
`x = +- (5pi)/6 + 2kpi`