Proof that (1+ sin(x))/(1 + 1/sin(x)) = sin(x)

You’re welcome

I put this into Wolfram Alpha today and was surprised to find it say sin(x). I had a rather complex way to solve it, but thanks to a comment below I now realize an easy way to show this is to multiply the top and bottom by sin(x):

Which is clearly just sin(x), since the fraction is 1. As they also pointed out, this does not depend on sin(x), and any function could have been put there.

This has been an unintended application of Cunningham’s law, where posting the wrong answer is more likely to get an author the correct answer than a simple question.