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Solve the equation tan^2(x) = 3 for x in the interval [0, 2π].

Practice Questions

Q1
Solve the equation tan^2(x) = 3 for x in the interval [0, 2π].
  1. π/3
  2. 2π/3
  3. 4π/3
  4. 5π/3

Questions & Step-by-Step Solutions

Solve the equation tan^2(x) = 3 for x in the interval [0, 2π].
  • Step 1: Start with the equation tan^2(x) = 3.
  • Step 2: Take the square root of both sides to get tan(x) = ±√3.
  • Step 3: Identify the angles where tan(x) = √3. These angles are x = π/3 and x = 4π/3.
  • Step 4: Identify the angles where tan(x) = -√3. These angles are x = 2π/3 and x = 5π/3.
  • Step 5: List all the solutions: x = π/3, x = 4π/3, x = 2π/3, and x = 5π/3.
  • Step 6: Since we only need the solutions in the interval [0, 2π], we keep all four solutions.
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