Simplify the expression.
-$$\frac { \cos ^ { 2 } x + \sin ^ { 2 } x } { \cot ^ { 2 } x - \csc ^ { 2 } x }$$
A) $- 1$
B) $\csc x$
C) 1
D) $\sec x$

Question

Quizplus · Accepted Answer

The numerator simplifies to 1 due to the Pythagorean identity $\cos^2x + \sin^2x = 1$. The denominator simplifies to $-1$ because $\cot^2x - \csc^2x = \frac{\cos^2x}{\sin^2x} - \frac{1}{\sin^2x} = \frac{\cos^2x - 1}{\sin^2x} = -\frac{\sin^2x}{\sin^2x} = -1$ using the identity $\sin^2x + \cos^2x = 1$. Thus, the expression simplifies to $\frac{1}{-1} = -1$.

Simplify the Expression cos⁡2x+sin⁡2xcot⁡2x−csc⁡2x\frac { \cos ^ { 2 } x + \sin ^ { 2 } x } { \cot ^ { 2 } x - \csc ^ { 2 } x }cot2x−csc2xcos2x+sin2x​

Simplify the Expression $\frac { \cos ^ { 2 } x + \sin ^ { 2 } x } { \cot ^ { 2 } x - \csc ^ { 2 } x }$