Final answer:
To solve the equation sin2x = 3cos2x, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1 and rearrange the equation. Simplify the equation and find the value of sin(x) to determine the solutions in the second and third quadrants.
Step-by-step explanation:
To solve the equation sin2x = 3cos2x, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1 and rearrange the equation:
sin^2(x) = 3(1 - sin^2(x))
Simplifying, we get 4sin^2(x) = 3. Solving for sin(x), we find sin(x) = ±√(3/4).
Since we're looking for solutions in the second and third quadrants, we'll take the negative square root and find x = 210° in the second quadrant and x = 330° in the third quadrant.