Answer
$\frac{sin~x}{1-cos~x} = cot~\frac{x}{2}$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/afdfaf4f-7422-46de-94ce-b9b6030ba7b5/result_image/1555426481.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001113Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=fa82f2878eb9f25b19b82a6f5c9159837909147abd626418a9e26a56d38e4220)
Work Step by Step
$\frac{sin~x}{1-cos~x}$
When we graph this function, it looks like the graph of $~~cot~\frac{x}{2}$
We can verify this algebraically:
$\frac{sin~x}{1-cos~x}$
$=\frac{1}{\frac{1-cos~x}{sin~x}}$
$=\frac{1}{tan~\frac{x}{2}}$
$=cot~\frac{x}{2}$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/afdfaf4f-7422-46de-94ce-b9b6030ba7b5/steps_image/small_1555426481.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T001113Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=5af75140e4b830869a9c989bf686464bb61f630fdf2378ab20ee7e3fb7d620a8)