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## Homework Statement

[tex]\lim_{h\rightarrow0}= \frac{tan(\frac{\pi}{4}+2h)\ - tan\frac{\pi}{4}}h[/tex]

## The Attempt at a Solution

Here's what i was able to work out.

Use the trig addition formula:

[tex]\lim_{h\rightarrow0}= \frac{(\frac{tan\frac{\pi}{4}+ tan2h}{1-tan\frac{\pi}{4}tan2h}) - tan\frac{\pi}{4}}h[/tex]

Get the LCD of 1 - tan(pi/4)tan2h, then multiply by 1 - tan(pi/4)tan2h to get rid of the fraction.

[tex]\lim_{h\rightarrow0} = \frac{tan\frac{\pi}{4} + tan2h - tan\frac{\pi}{4}(1 - tan\frac{\pi}{4}tan2h)} {h(1- tan\frac{\pi}{4}tan2h)}[/tex]

The last two terms cancel out:

[tex]\lim_{h\rightarrow0} = \frac{tan\frac{\pi}{4} + tan2h - tan\frac{\pi}{4}}h[/tex]

You're left with:

[tex]\lim_{h\rightarrow0} = \frac{tan2h}h[/tex]

Then i believe you would need to use the double angle formula?

[tex]\lim_{h\rightarrow0} = \frac{\frac{2tanh}{1-tan^2h}}h[/tex]

multiply to get rid of fraction

[tex]\lim_{h\rightarrow0} = \frac{2tanh}{h(1 - tan^2h)}[/tex]

And this is where I got stuck, any suggestions?