Complete the identity.
-The expression $\frac { \cos \theta - \sin ^ { 2 } \theta } { \cos \theta } \cdot \csc \theta$
is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be u: the right hand side of the equation to complete the identity?
A) $\tan ^ { 2 } \theta$
B) $\cos \theta = 1$
C) $\sec \theta + \cos \theta$
D) $\csc \theta - \tan \theta$

Question

Quizplus · Accepted Answer

The given expression simplifies to $\csc \theta - \tan \theta$. First, divide $\cos \theta - \sin^2 \theta$ by $\cos \theta$ to get $1 - \sin^2 \theta / \cos \theta$, which simplifies to $1 - \tan^2 \theta$ using the Pythagorean identity. Multiplying by $\csc \theta$ gives $\csc \theta - \tan \theta$.

Complete the Identity cos⁡θ−sin⁡2θcos⁡θ⋅csc⁡θ\frac { \cos \theta - \sin ^ { 2 } \theta } { \cos \theta } \cdot \csc \thetacosθcosθ−sin2θ​⋅cscθ

Complete the Identity $\frac { \cos \theta - \sin ^ { 2 } \theta } { \cos \theta } \cdot \csc \theta$