Answer
$\frac{1-cos~2x}{sin~2x} = tan~x$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3b0b6924-04f8-4bb3-b3ec-7a8efdad2341/result_image/1555423567.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012301Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=d972e2b08b642df04211efc3d2ae6e19bafaddd0ce5ede5a72ae479ada1f83ff)
Work Step by Step
$\frac{1-cos~2x}{sin~2x}$
When we graph this function, it looks like the graph of $~~tan~x$
We can verify this algebraically:
$\frac{1-cos~2x}{sin~2x}$
$= \frac{1-(1-2~sin^2~x)}{2~sin~x~cos~x}$
$= \frac{2~sin^2~x}{2~sin~x~cos~x}$
$= \frac{sin~x}{cos~x}$
$= tan~x$
![](https://gradesaver.s3.amazonaws.com/uploads/solution/3b0b6924-04f8-4bb3-b3ec-7a8efdad2341/steps_image/small_1555423567.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T012301Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=d90116f13c75b4ccb89fcd7300a371246d67de4d566a4edeca9169e208e89df6)