Question

How do you solve `6tan^2x-2=4` for `0<=x<=2pi`?

Answer 1

`x in {pi/4, (3pi)/4, (5pi)/4, (7pi)/4}`

Explanation:

`6tan^2(x)-2=4`

`rarr 6tan^2(x)=6`

`rarr tan^2(x)=1`

`rarr tan(x)= +-1`

That is using a unit circle, the opposite and adjacent sides are of equal length, giving the 4 possibilities identified above.