Determine if the following is an identity.
-$$\frac { 1 + \csc x } { \sec x } = \cos x + \cot x$$
A) Identity
B) Not an identity

Question

Quizplus · Accepted Answer

To verify if the given equation is an identity, we can simplify the left side and see if it equals the right side. The left side is $\frac { 1 + \csc x } { \sec x }$. We know that $\csc x = \frac{1}{\sin x}$ and $\sec x = \frac{1}{\cos x}$. Substituting these into the left side gives us $\frac { 1 + \frac{1}{\sin x} } { \frac{1}{\cos x} }$ which simplifies to $\cos x + \frac{\cos x}{\sin x}$. Since $\frac{\cos x}{\sin x} = \cot x$, the left side simplifies to $\cos x + \cot x$, which is exactly the right side. Therefore, the given equation is an identity.

Determine If the Following Is an Identity 1+csc⁡xsec⁡x=cos⁡x+cot⁡x\frac { 1 + \csc x } { \sec x } = \cos x + \cot xsecx1+cscx​=cosx+cotx

Determine If the Following Is an Identity $\frac { 1 + \csc x } { \sec x } = \cos x + \cot x$