SOLUTION: Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.) 2 tan(x) = 1 − tan^2(x)

Question 1078822: Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)
2 tan(x) = 1 − tan^2(x)
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
2 tan(x) = 1 - tan^2(x)
tan^2 + 2tan - 1 = 0
Sub x for tangent
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=8 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:

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tan(x) = sqrt(2) - 1
tan(x) = -sqrt(2) - 1
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Find x with a calculator

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SOLUTION: Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.) 2 tan(x) = 1 − tan^2(x)