Prove sinx+cosx=x has a single solution

[mystmyst]

Homework Statement

Prove sinx+cosx=x has a single solution in [0, pi/2]

The Attempt at a Solution

This question seems very strange to me. How can I prove there is a single solution for every number between 0 and pi/2?

I'm not sure what formula to use.
I'm learning infinitesimal math.

Can someone help me out?
Thanks!

 

[D H]

This question seems very strange to me. How can I prove there is a single solution for every number between 0 and pi/2?

You are misreading the problem. You aren't supposed to show that that is "a single solution for every number between 0 and pi/2". In other words, you are supposed to show that there is

1. A point x somewhere between 0 and pi/2 at which sinx+cosx=x.
2. There are no other solutions in this interval.

 

[madah12]

Homework Statement

Prove sinx+cosx=x has a single solution in [0, pi/2]

The Attempt at a Solution

This question seems very strange to me. How can I prove there is a single solution for every number between 0 and pi/2?

I'm not sure what formula to use.
I'm learning infinitesimal math.

Can someone help me out?
Thanks!

I think you should use the intermediate value theorem to prove there is atleast one solution and rolles theorem to show that there can't be more than one solution.