The student did not make a mistake. Answer was correct.
How to analyze trigonometric functions
In this question we must simplify a given trigonometric expression and find if answer is the same of that from student. We must apply all properties of trigonometric functions and real algebra:
[tex]\frac{\sin 2x}{\cos x} = 2[/tex]
[tex]\sin 2x = 2\cdot \cos x[/tex]
[tex]2\cdot \sin x \cdot \cos x = 2\cdot \cos x[/tex]
[tex]\sin x = 1[/tex]
[tex]x = \frac{\pi}{2}[/tex]
Albeit cosine is undefined at [tex]x = \frac{\pi}{2}[/tex], this discontinuity is evitable by canceling terms. The expression is equivalent to [tex]f(x) = 2\cdot \sin x[/tex], which is continuous for all [tex]x\in \mathbb{R}[/tex]. According to this result, the student did not make a mistake. Answer was correct. [tex]\blacksquare[/tex]
To learn more on trigonometric functions, we kindly invite to check this verified question: https://brainly.com/question/6904750
