Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression.
-$$\frac { \sin ^ { 2 } x - 1 } { \cos ( - x ) }$$
A) $- \cos x$
B) $\cos x$
C) $\sin x$
D) $- \sin x$

Question

Quizplus · Accepted Answer

The expression can be simplified using the Pythagorean identity $\sin^2 x + \cos^2 x = 1$, which can be rearranged to $\sin^2 x - 1 = -\cos^2 x$. Thus, the expression becomes $\frac{-\cos^2 x}{\cos(-x)}$. Since $\cos(-x) = \cos x$, the expression simplifies to $-\cos x$.

Write the Expression in Terms of Sine and Cosine, and Simplify