identity (mathematics); equation that holds true for all values
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Meanings
1 sense · 4 examplesnoun
identity; an equation that is true for all values of its variables
formalA fundamental concept in algebra and trigonometry. Often denoted with the symbol '≡' (identity sign) to distinguish from conditional equations.
Gōu勾
gǔ股
dìng定
lǐ理
a²
+a
b²²
=
c²+
shì
shìb
yòng²
yú
zhí=
jiǎo
sānc
jiǎo²
xíng
de是
héng适
děng用
shì于
直
角
三
角
形
的
恒
等
式
。
The Pythagorean theorem a² + b² = c² is an identity that holds for right triangles.
Lǎo老
shī师
ràng让
wǒ我
men们
zhèng证
míng明
zhè这
gè个
sān三
jiǎo角
héng恒
děng等
shì式
：
sin²θs
+i
cos²θn
=²
1θ
+
c
o
s
²
θ
=
1
。
The teacher asked us to prove this trigonometric identity: sin²θ + cos²θ = 1.
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(
xx
+
y+
²
=y
)
x²²
+
2=
x
yx
+²
y²
shì+
yī
gè2
jīx
běny
de
dài+
shù
héngy
děng²
shì
是
一
个
基
本
的
代
数
恒
等
式
。
(x + y)² = x² + 2xy + y² is a basic algebraic identity.
Zài在
shù数
xué学
tuī推
dǎo导
zhōng中
，
jīng经
cháng常
lì利
yòng用
héng恒
děng等
shì式
jìn进
xíng行
huà化
jiǎn简
。
In mathematical derivations, identities are often used for simplification.