Complete the identity.
-$\cot \frac { \theta } { 2 } = ?$
A) $\frac { \sin \theta } { 1 - \cos \theta }$
B) $\frac { \sin \theta } { 1 + \cos \theta }$
C) $\frac { \sin \theta } { \sin \theta - \cos \theta }$
D) $\frac { \sin \theta } { \sin \theta + \cos \theta }$

Question

Quizplus · Accepted Answer

The correct identity for $\cot \frac{\theta}{2}$ is $\frac{1 + \cos \theta}{\sin \theta}$, which can be rewritten as $\frac{\sin \theta}{1 - \cos \theta}$ by using the reciprocal identity $\cot \theta = \frac{1}{\tan \theta}$ and the half-angle identity for $\tan \frac{\theta}{2}$. Therefore, option A is correct.

Complete the Identity cot⁡θ2=?\cot \frac { \theta } { 2 } = ?cot2θ​=?

Complete the Identity $\cot \frac { \theta } { 2 } = ?$