Show that tan: (-pie/2,pie/2)->R is a homeomorphism where tan = sin/cos(adsbygoogle = window.adsbygoogle || []).push({});

To show that f and f^-1 are cts, it seems trivial from a sketch but how do you do it?

For 1-1 tan(x) = tan(y)

Need to knwo x =y

tan(x) = sinx.cosx = siny/cosy = tany

=> sixcosy = sinycosx

this gets you sin(x-y) = 0

But x-y = pie

What's wrong here?

Onto is obvious

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# Sin t = 0 homeomorphism

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