- #1

- 612

- 49

## Homework Statement

Find the Maclaurin series for (tanx)

^{2}

## Homework Equations

[tex]f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2}+...[/tex]

## The Attempt at a Solution

I don't see how it's reasonable to do this problem without using a computer.

The derivative of (tanx)

^{2}is 2tanxsec

^{2}x, then the derivative of that is -2(cos2x-2)sec

^{4}x, then the derivative of that is -2(sin3x-11sinx)sec

^{5}x.

Going up to only the third derivative is pretty difficult, but just going that far doesn't give me much information about the series. It only gives me x

^{2}, because the other terms are 0.

So is there another way of doing this, or is deriving these long expressions the only way?

Thanks.