Final answer:
To solve the equation 2tan(3x - π/5) = 1, divide both sides by 2 and take the inverse tangent of both sides. Solve for x to find the answer.
Step-by-step explanation:
To solve the equation 2tan(3x - π/5) = 1, we need to isolate the variable x. First, we can divide both sides of the equation by 2 to get tan(3x - π/5) = 1/2. Next, we can take the inverse tangent (tan⁻¹) of both sides to find the angle. The inverse tangent of 1/2 is approximately 0.464 radians or π/6. Solving for x, we can set 3x - π/5 equal to π/6 and solve for x. Adding π/5 to both sides gives us 3x = π/6 + π/5. Combining the fractions gives us 3x = (5π + 6π)/30 or 3x = 11π/30. Dividing both sides by 3 gives us x = 11π/90 or x = π/30. Therefore, the correct answer is (a) x = π/3.