Prove 1+1=2 using trigonometric functions

Click For Summary

Discussion Overview

The discussion centers around the question of whether it is possible to prove that 1 + 1 = 2 using trigonometric functions. Participants explore the implications of such a requirement, questioning its validity and purpose, while also discussing the relationship between trigonometric identities and basic arithmetic.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant questions the relevance of trigonometric functions in proving 1 + 1 = 2, suggesting it makes no sense.
  • Another participant acknowledges the oddity of the requirement but proposes that if trigonometric identities are allowed, one must consider whether those identities can be derived without using basic addition to avoid circular reasoning.
  • A participant humorously suggests that using a trigonometric identity could lead to the incorrect conclusion that 1 + 1 = 1 for a sufficiently large value of 1.
  • There is a correction made to a trigonometric identity provided earlier, indicating the importance of accuracy in mathematical expressions.
  • Some participants assert that proving 1 + 1 = 2 is typically done in set theory or mathematical logic, not through trigonometric functions.
  • Concerns are raised about the original poster's intentions, with some participants suspecting trolling due to the vagueness of the question and lack of clarification.
  • One participant explicitly asks for the reasoning behind the question, expressing skepticism about its legitimacy as a textbook problem.

Areas of Agreement / Disagreement

Participants generally disagree on the feasibility and appropriateness of using trigonometric functions to prove 1 + 1 = 2. There is no consensus on the purpose of the original question or whether it is a legitimate mathematical inquiry.

Contextual Notes

Some participants highlight the potential circular reasoning involved in using trigonometric identities to prove basic arithmetic, indicating a limitation in the approach suggested by the original poster.

jontyjashan
Messages
68
Reaction score
0
Prove
1+1=2
using trigonometric functions
 
Physics news on Phys.org


That makes no sense. Why on Earth would you think that trigonometric functions are involved in the proof of 1 + 1 = 2?
 


Bit of an odd requirement, but I guess if you're allowed to use trig identities you can do it. The problem is though can we derive those identities without using simple addition in the first place, therefore do it without circular reasoning.

What is the purpose of this exercise, are you studying trigonometric identities? If this is an exercise to test your knowledge of trigonometry you could for example use:
<br /> \cos x +\cos y=2\cos((x+y)/2)\cos((x-y)/2)<br />
 
Last edited:


Cyosis said:
Bit of an odd requirement, but I guess if you're allowed to use trig identities you can do it. The problem is though can we derive those identities without using simple addition in the first place, therefore do it without circular reasoning.

What is the purpose of this exercise, are you studying trigonometric identities? If this is an exercise to test your knowledge of trigonometry you could for example use:
<br /> \cos x +\cos y=\cos((x+y)/2)\cos((x-y)/2)<br />

This proves 1 + 1 = 1
:-)
 


mma said:
This proves 1 + 1 = 1
:-)

... for a sufficiently large value of 1.
 


Whoops, let's be glad the formula I listed is wrong or we would be in trouble!

I forgot a factor of two it should of course be.

<br /> \cos x +\cos y=2\cos((x+y)/2)\cos((x-y)/2)

Fixed it in the original post as well.
 


how this proves 1+1=2
give detail
 


You don't prove 1+1=2 using trigonometric functions. You do that in set theory, or math logic.
 


troll
 
  • #10


jontyjashan said:
how this proves 1+1=2
give detail

Substitute x = y = 0.
 
  • #11


I am kind of starting to suspect this he is a troll as well. If you look at all his other topics, every post is vague, borderline preposterous and when asked to clarify he never bothers to do so.
 
  • #12


i m not a troll
 
  • #13


Then could you explain the reason behind this question perhaps? I have a hard time believing this is a textbook problem.
 
  • #14


this is not a textbook question
 
  • #15


Then what kind of question is it? Why are you insisting that a proof of such a fundamental property (it really is, basically, the definition of "2") use such sophisticated tools as trig functions?
 

Similar threads

MHB HIGHLY Rigorous Treatment of the Trigonometric Functions
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Elliptic Function Rotation Problem
  • · Replies 1 ·
Replies
1
Views
2K
High School Can 2(sinx) be called a 'trigonometric function'?
  • · Replies 28 ·
Replies
28
Views
3K
Undergrad Units of trigonometric functions?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Finding the inverse tangent of a complex number
  • · Replies 3 ·
Replies
3
Views
4K
Roots of a polynomial mixed with a trigonometric function
  • · Replies 14 ·
Replies
14
Views
2K
High School Trigonometric substitution, a case I'd like to share
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Is the equation Velocity = Distance * Trigonometric Function valid in physics?
  • · Replies 9 ·
Replies
9
Views
2K
Inverse trigonometric functions
  • · Replies 6 ·
Replies
6
Views
2K
Analysis What’s a good book on transcendental functions?
  • · Replies 1 ·
Replies
1
Views
2K