you made an error here: u(u+1)=2
you needed to use u^2+u-2=0 and factor it completely
here is how I did it:
sec^2(x)+tan(x)=3
use Pythagorean identity sec^2(x)-tan^2(x)=1 =>sec^2(x)=tan^2(x)+1
tan^2(x)+1+tan(x)=3
tan^2(x)+1+tan(x)-3=0
tan^2(x)+tan(x)-2=0.......factor
(tan(x) - 1) (tan(x) + 2) = 0
solutions:
if tan(x) - 1= 0 =>tan(x) = 1
if tan(x) + 2= 0=>tan(x) =- 2
use inverse to find x
x = tan^-1(1)=π/4
x = tan^-1(-2)=-1.10715
general solutions are
Radians:
x=pi/4+pi*n
x=-1.10715 +pi*n
Degrees:
x=45° +180°*n,
x=-63.43494°+180°*n
