SOLUTION: Solve for x: sec^2 x + tanx = 3 0<<x<<360

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Question 1040633: Solve for x:
sec^2 x + tanx = 3 0<
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Definition: sec%28x%29=1%2Fcos%28x%29

Basic Identity: cos%5E2%28x%29%2Bsin%5E2%28x%29=1



1%2Btan%5E2%28x%29=sec%5E2%28x%29


Given Equation: sec%5E2%28x%29%2Btan%28x%29=3, along with 0%3Cx%3C360.
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1%2Btan%5E2%28x%29%2Btan%28x%29=3

tan%5E2%28x%29%2Btan%28x%29-2=0
-
tan%28x%29=%28-1%2B-+sqrt%281%5E2-4%2A%28-2%29%29%29%2F2

tan%28x%29=%28-1%2B-+sqrt%281%2B8%29%29%2F2

tan%28x%29=%28-1%2B-+3%29%2F2

system%28tan%28x%29=-2%2COR%2Ctan%28x%29=1%29

Your assigned domain will give about four different solutions.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for x:
sec^2 x + tanx = 3; 0 < x < 360
tan%5E2+%28x%29+%2B+1+%2B+tan+%28x%29+=+3 ------ Substituting matrix%281%2C3%2C+tan%5E2+%28x%29+%2B+1%2C+for%2C+sec%5E2+%28x%29%29

tan%5E2+%28x%29+%2B+tan+%28x%29+-+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%28matrix%281%2C3%2C+tan+%28x%29+=+1%2C+or%2C+tan+%28x%29+=+-+2%29%29



tan (x) = 1 is in the 1st and 3rd quadrants, where tan is positive (> 0), so 



tan (x) = - 2 is in the 2nd and 4th quadrants, where tan is negative (< 0), so