It is proved that when x is very small, 1 / (1 + x ^ 2) is about 1-x ^ 2 Seek guidance

It is proved that when x is very small, 1 / (1 + x ^ 2) is about 1-x ^ 2 Seek guidance

1/(1+x²)=1-x²+x^4-x^6+...≈1-x²
If the absolute value of X is very small, the terms above the fourth power can be ignored

How to prove that 1 / x + X is greater than or equal to 2

First of all, X must be greater than 0, otherwise the problem is impossible,
When x > 0
Because (1 / x-x) ^ 2 ≥ 0
I.e. 1 / x ^ 2 + x ^ 2-2 ≥ 0
Four on both sides
1/x^2+x^2+2≥4
I.e. (1 / x + x) ^ 2 ≥ 4
So 1 / x + X ≥ 2

Given sin (α + Wu / 2) = 1 / 3, α∈ (- Wu / 2,0), then Tan α is equal to

Sin (α + Wu / 2) = 1 / 3 α∈ (- Wu / 2,0)
cosα=1/3
sina=-√1-(1/3)^2=-2√2/3
tanα=(-2√2/3) /(1/3)
tanα=-2√2