Final answer:
The student's trigonometric equation involving secant, cosecant, sine, and cosine functions of a negative angle has been simplified using trigonometric identities, revealing a potential error in the student's initial equation.
Step-by-step explanation:
The subject of the question is simplifying a trigonometric expression that involves secant, cosecant, sine, and cosine of a negative angle. The student is seeking to verify or correct the equation sec(-x) / csc(-x) * sin(-x) / cos(-x) = -2tan(x).
Through the use of trigonometric identities, we can manipulate the expression accordingly. We know that sec(x) = 1/cos(x) and csc(x) = 1/sin(x), and that sin(-x) = -sin(x) and cos(-x) = cos(x) due to the odd and even properties of the sine and cosine functions, respectively.
Thus, the given expression simplifies to -1/tan(x) which is not equal to -2tan(x). It seems there may be a mistake in the equation provided by the student.