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

Question

Quizplus · Accepted Answer

The given expression can be simplified using trigonometric identities. First, find a common denominator and combine the fractions:$$\frac { 1 } { 1 - \cos x } + \frac { 1 } { 1 + \cos x } = \frac { (1 + \cos x) + (1 - \cos x) } { (1 - \cos x)(1 + \cos x) }$$Simplify the numerator and the denominator:$$\frac { 2 } { 1 - \cos^2 x }$$Using the Pythagorean identity $\sin^2 x = 1 - \cos^2 x$, we can rewrite the expression as:$$\frac { 2 } { \sin^2 x }$$This is equivalent to $2 \csc^2 x$, which matches choice C.

Simplify the Expression 11−cos⁡x+11+cos⁡x\frac { 1 } { 1 - \cos x } + \frac { 1 } { 1 + \cos x }1−cosx1​+1+cosx1​

Simplify the Expression $\frac { 1 } { 1 - \cos x } + \frac { 1 } { 1 + \cos x }$