Idon’t understand the question can someone me ?

That "double" less than symbol is used to say "much smaller than". It is of course a qualitative symbol, and it has no rigorous definition.

The exercise asks you to verify, numerically, that if you choose a very, very small input, then the approximations are good. Take the first one for example: we claim that if we pick a very small angle, its cosine is almost one. Let's choose . If we compute its cosine, we have

So, approximating the result with 1 is a good approximation.

Similarly, in the second example, we claim that for very small angles, the sine of the angle is almost the angle itself: choosing for example , we have

So the output is almost identically to the input.

For the third, we claim that and are almost the same thing if x is very small. So, for example, we pick and we have

whereas

so the two results are almost identical.

You can keep going like this and "prove" all the remaining approximations