SOLUTION: Solve the equation when x is in the set of [0, 2(pi)). secx = 1 + tanx

Question 726610: Solve the equation when x is in the set of [0, 2(pi)).
secx = 1 + tanx
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve the equation when x is in the set of [0, 2(pi)).
secx = 1 + tanx
----
Multiply thru by cos(x) to get:
1 = cos + sin
1 = sqrt(1-sin^2) + sin
1-sin = sqrt(1-sin^2)
(1-sin)^2 = 1-sin^2
1 - 2sin + sin^2 = 1-sin^2
2sin^2 -2sin = 0
sin(2sin-2) = 0
sin(x) = 0 or sin(x) = 1
x = 0 or x = pi/2
Usable solution:
x = 0
Check
sec(0) = 1 + tan(0)
1 = 1 + 0
1 = 1
=============
Cheers,
Stan H.
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