Please prove the following trig identity and give a reason for each step in your proof.

Question

You have been hired by the Willy Wonka Candy Factory to design the skill testing question for their Golden

Ticket. This isn’t just any skill testing question. You have been asked to select a trig identity for contestants to solve. Please prove the following trig identity and give a reason for each step in your proof.

tanxsinx / tanx + sinx = tanx - sin x/ tanxsinx

For every solution, you must provide the following:

 A diagram showing how the given information is used

 A full solution, showing all work

 Any justification/explanation that may be required

 A final statement that answers the given question

Answer 1

desmos.com/calculator/ei3qfxtqj6

This video shows one way to prove the identity (without actually listing the reasons for every step).