Find the Maclaurin series for (tanx)2
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 2tanxsec2x, then the derivative of that is -2(cos2x-2)sec4x, then the derivative of that is -2(sin3x-11sinx)sec5x.
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 x2, because the other terms are 0.
So is there another way of doing this, or is deriving these long expressions the only way?