Diffeomorphisms | Mathematics | Page 1

sleek quiver Sep 10, 2025, 3:56 AM

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I have some trouble proving that tan x in (-pi/2,pi/2) is a diffeomorphism,specially in showing that tan x is C infinity, any suggestion?

gray ivyBOT Sep 10, 2025, 3:56 AM

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pine stream Sep 10, 2025, 5:50 AM

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@sleek quiver

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tanx=sinx .(1/cosx)

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since composition of two C^inf functions are also C^inf

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Let g=1/x and f=cosx then gf(x)=1/cosx is also C^inf

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Now product of two C^inf functions is also C^inf

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So sinx.gf(x) is also C^inf

sleek quiver Sep 10, 2025, 3:35 PM

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Oh that makes sense 😅, I was thinking in taking its derivatives

#Diffeomorphisms