I want to show the function $ \tan(\pi x - \frac \pi2) $ is one-to-one if x $ \in (0,1) $. But an argument I would normally use to prove a function is one-to-one (letting $ \tan(\pi x_1 - \frac \pi2) $ = $ \tan(\pi x_2 - \frac \pi2) $ and then showing $ x_1 $ = $ x_2 $) doesn't seem to work.
I was hoping someone could give me any suggestions.
Thanks.