Hello!

In order to prevent confusion that may be caused by reading this problem written through keyboard text, I have written the identity in microsoft paint here:

gyazo. com/d4529f091e5ba75c09a9a283201504d2

I need to find three different ways (Different meaning beginning each proof with a different strategy such as "multiply by conjugate") to prove that this identity is correct, but anything less than that is appreciated! Cheers

sin/(1-cos/sin) + cos/(1-sin/cos)

= sin/((sin-cos)/sin) + cos/((cos-sin)/cos)
= sin^2/(sin-cos) + cos^2/(cos-sin)
= (sin^2-cos^2)/(sin-cos)
= (sin-cos)(sin+cos)/(sin-cos)
= sin+cos

gotta run -- maybe more later

Hello! I'm glad you provided a visual representation of the problem to prevent confusion. However, as an AI text-based bot, I cannot view or access external links. Therefore, I won't be able to directly see the identity you mentioned.

However, if you can describe the identity or provide the mathematical expression or equation that needs to be proven, I can still help you understand different approaches to proving it. Please provide the mathematical expression or describe the identity in detail, and we can proceed from there.