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Show that f(x)=tanx is an increasing fun...

Show that `f(x)=tanx` is an increasing function on `(-pi//2,\ pi//2)` .

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We have given `f(x)=tanx`
Then
`f(x)=tanx`
`impliesf′(x)=sec^2x`
Now, `−pi/2`<`x`<`pi/2`
`impliessecx`>`0`
`impliessec^2x`>`0`
`impliesf′(x)`>`0`
...
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