# prove this quantity (1-x^2/2)<=cosx<= (1-x^2/2)+(x^4/4*3*2)

### 1 Answer | Add Yours

Remember that the values of cosine function are included in the interval [-1;1].

You must show that the inequality is true.

`1- (x^2/2) =lt cos x = lt 1- (x^2/2) + x^4/24`

Add the quantity `x^2/2` to the left and to the right of inequality, to keep it stable.

`1- (x^2/2)+ (x^2/2)=lt cos x = lt 1- (x^2/2) + (x^2/2) +x^4/24`

Yo may reduce the opposite terms:

`1=lt cos x = lt 1+x^4/24`

Notice that the left side is a false statement because the values of the cosine function do not overpass 1.

**ANSWER: The inequality is not true.**