An identity is a value and an operation such that applying the value and operation does not change the result.
The additive identity for real numbers is 0. This is because one can add 0 to any value, and the result is the same. Example: 3 + 0 = 3.
The multiplicative identity for real numbers is 1. This is because one can multiply 1 by any value, and the result is the same. Example: -5 · 1 = -5.
Identity | Description |
---|---|
a + 0 = a | The additive identity for real numbers is the number 0. This is because, for any real number a, a + 0 = a. |
a·1 = a | The multiplicative identity for real numbers is 1. You can see that a·1 = a. |
The identity for a square matrix under multiplication is a diagonal matrix where every diagonal value is 1. |
Equation | Description |
---|---|
sin(x)^{2}+sin(x) = 1-cos(x)^{2} | Equation to solve. |
sin(x)^{2}+cos(x)^{2}+sin(x) = 1 | Add cos(x)^{2} to both sides of the equations. |
1+sin(x) = 1 | Substitute 1 for sin(x)^{2}+cos(x)^{2}. |
sin(x) = 0 | Subtract 1 from both sides. |
x ∈ {0, π, 2π, 3π, ...} | Transform equation from trigonometric form to set form. |
Table 1: Using an identity to solve an equation. |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | Y |
Z | X |
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