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

1 answer

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