SOLUTION: I need to find all solutions of the equation 4 sec x + 4 tan x=4 in the interval [0, 2pi) algebraically

Question 888750: I need to find all solutions of the equation 4 sec x + 4 tan x=4 in the interval [0, 2pi) algebraically
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
4 sec x + 4 tan x=4
sec x + tan x = 1
1/cos + sin/cos = cos/cos
1 + sin = cos
1 + sin = sqrt(1 - sin^2)
sin^2 + 2sin + 1 = 1 - sin^2
2sin^2 + 2sin = 0
sin(sin + 1) = 0
sin = 0 --> x = 0, x = pi
x = pi --> 4*(-1) + 4*0 = 4 so is extraneous
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sin = -1 --> x = 3pi/2
@ x = 3pi/2 both sec and tan are undefined
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Only x = 0 works
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