To me the most common identity that comes to mind that results in 1 is...

PEEWSRIGWETRYqx

PEEWSRIGWETRYqx

Answered

2022-01-01

To me the most common identity that comes to mind that results in 1 is the trigonometric sum of squared cosine and sine of an angle:
cos2θ+sinθ=1 (1)
and maybe
eiπ=1 (2)
Are there other famous (as in commonly used) identities that yield 1 in particular?

Answer & Explanation

jgardner33v4

jgardner33v4

Expert

2022-01-02Added 35 answers

Pick your favorite probability density function f, then
f(x)dx=1
Tiefdruckot

Tiefdruckot

Expert

2022-01-03Added 46 answers

(xR)cosh2(x)sinh2(x)=1
Vasquez

Vasquez

Expert

2022-01-08Added 457 answers

Here are two well-known infinite series whose sum is 1:
n=112n=12+14+18+116+132+=1
n=11n(n+1)=112+123+134+145+156+=1
The following series is less known, interesting although:
n=11sn=12+13+17+143+11807+=1
where denominators form Sylvester sequence: every term is equal to the product of all previous terms, plus one. For example
2
3=2+1
7=2 * 3+1
43=2 * 3 * 7+1
1807=2 * 3 * 7 * 43+1
and so on

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