Question

Find all solutions of the equation in the interval [0,2pi)
8sec^2x+4tan^2x-12=0

Answer 1

π/6+2πk
5π/6+2πk
you need to factor and use trig identities

Answer 2

8(1+tan^2x)+4tan^2x-12=0.
8+12tan^2x-12=0
12tan^2x=4
tanx=1/sqrt(3)
x=atan(1/sqrt(3))
x=0.5236