Prove sinx+cosx=x has a single solution

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  • #1
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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!
 

Answers and Replies

  • #2
D H
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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.
 
  • #3
326
1

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.
 

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