Which of the following is equivalent to the given expression?
$\frac { \cos ^ { 2 } x } { 1 + \sin x }$
A) $\cot x \cos x + \tan x$
B) $\csc x + \cot x$
C) $1 - \sin x$
D) $\tan x + \cos x$
E) $\tan x \cot x - \sin x$

Question

Which of the following is equivalent to the given expression? 
$\frac { \cos ^ { 2 } x } { 1 + \sin x }$  
A)  $\cot x \cos x + \tan x$
B)  $\csc x + \cot x$
C)  $1 - \sin x$
D)  $\tan x + \cos x$
E)  $\tan x \cot x - \sin x$

Quizplus · Accepted Answer

Using the Pythagorean identity $\cos^2x = 1 - \sin^2x$, we can rewrite the given expression as $\frac{1 - \sin^2x}{1 + \sin x}$. Factoring the numerator as a difference of squares gives $\frac{(1 - \sin x)(1 + \sin x)}{1 + \sin x}$, which simplifies to $1 - \sin x$.

Which of the Following Is Equivalent to the Given Expression cos⁡2x1+sin⁡x\frac { \cos ^ { 2 } x } { 1 + \sin x }1+sinxcos2x​

Which of the Following Is Equivalent to the Given Expression $\frac { \cos ^ { 2 } x } { 1 + \sin x }$