Prove 1+1=2 using trigonometric functions

Prove
1+1=2
using trigonometric functions

Answers and Replies

dx
Homework Helper
Gold Member

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

Cyosis
Homework Helper

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:
$$\cos x +\cos y=2\cos((x+y)/2)\cos((x-y)/2)$$

Last edited:

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:
$$\cos x +\cos y=\cos((x+y)/2)\cos((x-y)/2)$$

This proves 1 + 1 = 1
:-)

sylas
Science Advisor

This proves 1 + 1 = 1
:-)

... for a sufficiently large value of 1.

Cyosis
Homework Helper

Whoops, lets 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.

$$\cos x +\cos y=2\cos((x+y)/2)\cos((x-y)/2)$$

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

how this proves 1+1=2
give detail

Substitute x = y = 0.

Cyosis
Homework Helper

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.

i m not a troll

Cyosis
Homework Helper

Then could you explain the reason behind this question perhaps? I have a hard time believing this is a text book problem.

this is not a textbook question

HallsofIvy
Science Advisor
Homework Helper

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?