Complete the sentence so the result is an identity. Let x be any real number.
-Write $\cot x$ in terms of $\sin x$.
A) $\frac { \pm \sqrt { 1 - \sin ^ { 2 } x } } { 1 - \sin ^ { 2 } x }$
B) $\frac { \pm \sqrt { 1 - \sin ^ { 2 } x } } { \sin x }$
C) $\pm \sqrt { 1 - \sin ^ { 2 } x }$
D) $\frac { \pm \sin x \sqrt { 1 - \sin ^ { 2 } x } } { 1 - \sin ^ { 2 } x }$

Question

Quizplus · Accepted Answer

$\cot x = \frac{1}{\tan x} = \frac{1}{\frac{\sin x}{\cos x}} = \frac{\cos x}{\sin x}$. Using the Pythagorean identity, $\cos^2 x = 1 - \sin^2 x$, we can write $\cot x = \frac{\sqrt{1 - \sin^2 x}}{\sin x}$.

Complete the Sentence So the Result Is an Identity cot⁡x\cot xcotx

Complete the Sentence So the Result Is an Identity $\cot x$