# proving x.(3+cosx)>2sinx

#### emreyunus

##### New member
x.(3+cosx)>2sinx , x>0 I should solve this problem with mean value teorem and I am not sure how to because of x>0 but not x>=0.

#### Subhotosh Khan

##### Super Moderator
Staff member
x.(3+cosx)>2sinx , x>0 I should solve this problem with mean value theorem and I am not sure how to because of x>0 but not x>=0.
Note that:

3 + cos(x) >= 2

Please show us what you have tried and exactly where you are stuck.​
Please follow the rules of posting in this forum, as enunciated at:​

Last edited:

#### emreyunus

##### New member
Note that:

3 + cos(x) >= 2

Please show us what you have tried and exactly where you are stuck.​
Please follow the rules of posting in this forum, as enunciated at:​
okay, after applying this I could show that sinx<x for x>0 and its done, thanks

#### Jomo

##### Elite Member
okay, after applying this I could show that sinx<x for x>0 and its done, thanks
Maybe so, but you are required to use the mean value theorem.

#### emreyunus

##### New member
okay, after applying this I could show that sinx<x for x>0 and its done, thanks
I have a similiar question but this time that rule seems like can not help. Then how we can prove x.(2+cosx)>3sinx

#### emreyunus

##### New member
Maybe so, but you are required to use the mean value theorem.
yes, that's how I proved it

#### JeffM

##### Elite Member
I have a similiar question but this time that rule seems like can not help. Then how we can prove x.(2+cosx)>3sinx
You cannot prove that because it is not true.

$$\displaystyle 0\{2 + cos(0)\} = 0(2 + 1) = 0 * 3 = 0 \not > 0 = 3sin(0).$$

#### emreyunus

##### New member
You cannot prove that because it is not true.

$$\displaystyle 0\{2 + cos(0)\} = 0(2 + 1) = 0 * 3 = 0 \not > 0 = 3sin(0).$$
yes, sorry I didnt mention x>0 again