Question

How do you solve `sec(2x + pi/3) = 2/sqrt(3)`?

Answer 1

`-pi/12 and -pi/4`

Explanation:

Transform the equation to variable cos (2x + pi/3):
`1/(cos ((2x + pi)/3)) = 2/sqrt3`. Cross mulyiply:
`2cos (2x + pi/3) = sqrt3`
`cos (2x + pi/3) = sqrt3/2`
Trig table and unit circle -->
`2x + pi/3 = +- pi/6`
a. `2x + pi/3 = pi/6 --> 2x = pi/6 - pi/3 = - pi/6 --> x = - pi/12`
b. `2x + pi/3 = -pi/6 -> 2x = - pi/6 - pi/3 = - pi/2 --> x = -pi/4`