∀x ∈ [0, π] , 1 − x22 ⩽ cos x ⩽ 1 − x22 + x424

The given statement is a mathematical inequality involving trigonometric and polynomial functions. It states that for all x in the interval [0, π], the value of cos(x) is bounded by the values of two quadratic functions.

Here's how you can understand this inequality step by step:

1. The symbol "∀" stands for "for all". So, the inequality is true for all x in the interval [0, π].

2. The "∈" symbol means "in" or "belongs to". So, x belongs to the interval [0, π].

3. The inequality "1 − x^2/2 ⩽ cos x ⩽ 1 − x^2/2 + x^4/24" means that the value of cos(x) is greater than or equal to the value of the function 1 - x^2/2 and less than or equal to the value of the function 1 - x^2/2 + x^4/24.

4. The functions 1 - x^2/2 and 1 - x^2/2 + x^4/24 are both quadratic functions, which means they are polynomials of degree 2.

5. The function cos(x) is a trigonometric function, which oscillates between -1 and 1 for all real values of x.

6. The inequality is saying that within the interval [0, π], the value of cos(x) is always between the values of the two quadratic functions.

This inequality is a way of bounding the value of the cosine function using two simpler functions. It's a useful technique in mathematical analysis and can help to understand the behavior of the cosine function within the specified interval.