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Solve the equation tan^2(x) = 3.

Practice Questions

Q1
Solve the equation tan^2(x) = 3.
  1. x = π/3
  2. x = 2π/3
  3. x = 4π/3
  4. x = 5π/3

Questions & Step-by-Step Solutions

Solve the equation tan^2(x) = 3.
  • 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: Find the angles where tan(x) = √3. This occurs at x = π/3 + kπ, where k is any integer.
  • Step 4: Find the angles where tan(x) = -√3. This occurs at x = 2π/3 + kπ, where k is any integer.
  • Step 5: Combine the solutions from Steps 3 and 4. For k = 0, the solutions are x = π/3 and x = 2π/3.
  • Step 6: For k = 1, the solutions are x = π/3 + π = 4π/3 and x = 2π/3 + π = 5π/3.
  • Step 7: List the solutions: x = π/3, 4π/3, 2π/3, and 5π/3.
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