Simplify the expression.
-$$\frac { \cos x } { \tan ^ { 2 } x } - \frac { \cos x } { \sin ^ { 2 } x }$$
A) $- \cos x$
B) $- \sin x$
C) $\sin x$
D) $\cos x$

Question

Quizplus · Accepted Answer

The expression simplifies by recognizing that $\tan^2x = \frac{\sin^2x}{\cos^2x}$. Thus, the expression becomes $\frac{\cos x}{\frac{\sin^2x}{\cos^2x}} - \frac{\cos x}{\sin^2x} = \frac{\cos^3x}{\sin^2x} - \frac{\cos x}{\sin^2x}$. Factoring out $\frac{\cos x}{\sin^2x}$, we get $\frac{\cos x(\cos^2x - 1)}{\sin^2x}$. Since $\cos^2x - 1 = -\sin^2x$, the expression simplifies to $-\cos x$.

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Simplify the Expression $\frac { \cos x } { \tan ^ { 2 } x } - \frac { \cos x } { \sin ^ { 2 } x }$