Question 1040633

Solve for x:

sec^2 x + tanx = 3; 0 < x < 360
<pre>{{{tan^2 (x) + 1 + tan (x) = 3}}} ------ Substituting {{{matrix(1,3, tan^2 (x) + 1, for, sec^2 (x))}}}
{{{tan^2 (x) + tan (x) - 2 = 0}}} ------ Subtracting 3 from each side
(tan x - 1)(tan x + 2) = 0
tan x - 1 = 0       OR        tan x + 2 = 0
{{{highlight_green(matrix(1,3, tan (x) = 1, or, tan (x) = - 2))}}}

tan (x) = 1 is in the 1st and 3rd quadrants, where tan is positive (> 0), so {{{highlight_green(matrix(1,3, tan (x) = 1 = pi/4 = 45^o, or, 5pi/4 = 225^o))}}}

tan (x) = - 2 is in the 2nd and 4th quadrants, where tan is negative (< 0), so {{{highlight_green(matrix(1,3, tan (x) = - 2 = 116.565^o, or, 296.565^o))}}}