Use the fundamental identities to simplify the expression.
-$$\frac { \cos ^ { 2 } \theta } { \sin ^ { 2 } \theta } + \csc \theta \sin \theta$$
A) $\csc ^ { 2 } \theta$
B) $\sec ^ { 2 } \theta$
C) 1
D) $\tan ^ { 2 } \theta$

Question

Quizplus · Accepted Answer

The expression simplifies using the identity $\cos^2\theta = 1 - \sin^2\theta$ and the definition of $\csc\theta = \frac{1}{\sin\theta}$. The first term simplifies to $\cot^2\theta$ and the second term simplifies to 1, resulting in $\cot^2\theta + 1 = \csc^2\theta$, using the Pythagorean identity.

Use the Fundamental Identities to Simplify the Expression cos⁡2θsin⁡2θ+csc⁡θsin⁡θ\frac { \cos ^ { 2 } \theta } { \sin ^ { 2 } \theta } + \csc \theta \sin \thetasin2θcos2θ​+cscθsinθ

Use the Fundamental Identities to Simplify the Expression $\frac { \cos ^ { 2 } \theta } { \sin ^ { 2 } \theta } + \csc \theta \sin \theta$