Use a sum or difference identity to find the exact value.
-$\frac { \sin ^ { 2 } x - 1 } { \cos ( - x ) }$
A) $- \cos x$
B) $\sin x$
C) $\cos x$
D) $- \sin x$

Question

Quizplus · Accepted Answer

The expression can be simplified using trigonometric identities. The numerator $\sin^2x - 1$ can be rewritten using the Pythagorean identity as $-\cos^2x$. The denominator $\cos(-x)$ is equal to $\cos(x)$ because cosine is an even function. Thus, the expression simplifies to $-\cos^2x / \cos x = -\cos x$.

Use a Sum or Difference Identity to Find the Exact sin⁡2x−1cos⁡(−x)\frac { \sin ^ { 2 } x - 1 } { \cos ( - x ) }cos(−x)sin2x−1​

Use a Sum or Difference Identity to Find the Exact $\frac { \sin ^ { 2 } x - 1 } { \cos ( - x ) }$