Question 141791: Find all solutions of the equations in the interval [0, 2π) algebraically.
sec˛x – secx = 2
Answer by nabla(475)   (Show Source):
You can put this solution on YOUR website! sec˛x – secx -2 =0
let z=sec x
z^2-z-2=0
(z-2)(z+1)=0
gives z=2 or z=-1
which is to say, sec x=2 or sec x=-1.
Now, sec x=1/(cos x)
When does 1/(cos x)=2 ???
When does 1/(cos x)=-1 ???
This is the same as asking when does cos x=1/2 or -1.
Interval [0, 2π) is a full unit circle except for the 360 degree mark.
Cos x=1/2 at 60 degrees and 300 degrees.
Cos x=-1 at 180 degrees.
In radians, x=π/3, x=π, x=5π/6.
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