Question

How do you solve `2tan^4x - tan^2x - 15 = 0`?

Answer 1

Substitution
`y = tan^2 x`
then we have

`2y^2-y-15=0`
`2y^2 - 6y+5y-15=0`
`2y(y-3)+5(y-3) = 0`
`(2y+5)(y-3)=0`
`y=tan^2x=-5/2;3`

Proceed for solving `tan^2x`