Power series question involving classical mechanics

[seboastien]

Homework Statement

A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side.
From classical mechanics, TcosX= W and TsinX=F. Find F/W as a power series of X(angle).

Often in a problem like this, what we know is not X, but x(displacement) and l(length of string).

Find F/W as a series of powers in x/l

Homework Equations

TcosX=W
TsinX=F

The Attempt at a Solution

How do I calculate the power series for tanX? I've searched online but the people at yahoo answers got it wrong
http://en.wikipedia.org/wiki/Taylor_series
Wikipedia gives the answer but no route to it.

SinX= x/l

cosX= ((l-x)(l+x))^0.5/l

F/W = x/(l-x)(l+x)^0.5?

 

[vela]

You want things in terms of x/l. The sine already is, but the cosine isn't. Rewrite it slightly, like this

$$\cos X = \frac{\sqrt{l^2-x^2}}{l}} = \sqrt{1-\left(\frac{x}{l}\right)^2}$$

and go from there.