A student solved the equation Start Fraction sine 2 x over cosine x End Fraction equals 2, 0 less than or equals x less than or equals pi, and found an answer of Start Fraction pi over 2 End Fraction. Describe the student's error.
The student's error lies in their solution to the equation. They found that when Start Fraction sine 2 x over cosine x End Fraction equals 2, the solution is x = Start Fraction pi over 2 End Fraction. However, this solution is incorrect because the given equation does not equal 2 when x = Start Fraction pi over 2 End Fraction. The correct solution to the equation may involve using trigonometric identities or solving further algebraically.
