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) $\sin x$
C) $- \sin x$
D) $\cos x$

Question

Quizplus · Accepted Answer

The expression can be simplified using the Pythagorean identity $\sin^2x + \cos^2x = 1$, which allows us to rewrite $\sin^2x - 1$ as $-\cos^2x$. Since $\cos(-x) = \cos(x)$ due to the even property of the cosine function, the expression simplifies to $-\cos^2x / \cos x = -\cos x$.

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