Loss of numerical precision

Suppose we wish to evaluate the function $$f(x)=\frac{1-\cos(x)}{\sin(x)},$$ for small values of $x$. Five leading digits. If we multiply the denominator and numerator with $1+\cos(x)$ we obtain the equivalent expression $$f(x)=\frac{\sin(x)}{1+\cos(x)}.$$

If we now choose $x=0.007$ (in radians) our choice of precision results in $$\sin(0.007)\approx 0.69999\times 10^{-2},$$ and $$\cos(0.007)\approx 0.99998.$$

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