Determine if the following is an identity.
-$$\frac { \sin x } { 1 - \cos x } + \frac { \sin x } { 1 + \cos x } = 2 \csc x$$
A) Not an identity
B) Identity

Question

Quizplus · Accepted Answer

The given expression can be simplified to show that it is indeed an identity. By finding a common denominator and simplifying, we can show that the left side of the equation equals the right side. Specifically, the common denominator for the two fractions on the left side is $(1 - \cos x)(1 + \cos x)$, which simplifies to $1 - \cos^2 x$, which is equal to $\sin^2 x$. Thus, the left side simplifies to $\frac{2\sin x}{\sin^2 x} = 2 \csc x$, proving the identity.

Determine If the Following Is an Identity sin⁡x1−cos⁡x+sin⁡x1+cos⁡x=2csc⁡x\frac { \sin x } { 1 - \cos x } + \frac { \sin x } { 1 + \cos x } = 2 \csc x1−cosxsinx​+1+cosxsinx​=2cscx

Determine If the Following Is an Identity $\frac { \sin x } { 1 - \cos x } + \frac { \sin x } { 1 + \cos x } = 2 \csc x$