## Based on Pythagorean Identities Which Equation is True

Pythagorean identities are a set of equations that are used in advanced math and geometry to prove theorems and solve equations. They are based on the fundamental principles of Pythagoras’ theorem and trigonometry. In this article, we will explore which equation is true based on these identities.

### Introduction

Based on Pythagorean Identities Which Equation is True ? that are used to solve problems in mathematics, especially in geometry. They are based on the fundamental principles of Pythagoras’ theorem and trigonometry. The identities can be used to prove theorems, solve equations, and simplify expressions. They are also used to find the area of a triangle and calculate the lengths of its sides.

#### Pythagorean Identities

The Pythagorean identities are a set of equations that are related to the Pythagorean theorem. They are:

- a^2 + b^2 = c^2
- a^2 – b^2 = (a+b)(a-b)
- (a+b)^2 = a^2 + 2ab + b^2
- (a-b)^2 = a^2 – 2ab + b^2

These equations are used to solve problems related to the Pythagorean theorem, such as finding the length of the sides of a triangle.

#### Equation Overview

The equation that is true based on the Pythagorean identities is:

a^2 + b^2 = c^2

This equation is the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This equation can be used to find the length of the sides of a triangle and prove theorems related to right triangles.

#### Proving the Equation

The equation can be proved using the Pythagorean identities. To prove the equation, we need to use the identity a^2 + b^2 = (a+b)(a-b). We can then substitute a+b for c and a-b for c, which gives us the equation a^2 + b^2 = c^2.

#### Pythagoras’ Theorem

Pythagoras’ theorem is the fundamental principle behind the **Pythagorean identities**. It states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This theorem can be used to prove the equation a^2 + b^2 = c^2.

#### Trigonometric Ratios

Trigonometric ratios are ratios of the sides of a right triangle. These ratios can be used to find the lengths of the sides of a triangle. The most common ratios are sine, cosine, and tangent.

#### Cosine Rule

The cosine rule is a trigonometric equation that states that the square of the length of a side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of their lengths multiplied by the cosine of the angle between them. This equation can be used to find the length of the sides of a triangle.

##### Sine Rule

The sine rule is similar to the cosine rule, but it states that the ratio of the lengths of the sides of a triangle is equal to the ratio of the sines of the angles opposite those sides. This equation can also be used to find the length of the sides of a triangle.

##### Quadratic Equations

Quadratic equations are equations that involve terms of the second degree. These equations can be solved using the quadratic formula, which states that the solutions of a quadratic equation are the roots of the equation.

##### Quadratic Formula

The quadratic formula is used to solve quadratic equations. It states that the solutions of a quadratic equation are the roots of the equation. The formula is: x = (-b ± √(b² – 4ac)) / 2a.

###### Simplifying the Equation

The equation can be simplified by substituting a+b for c and a-b for c, which gives us the equation a^2 + b^2 = c^2. This equation can be used to find the length of the sides of a triangle and prove theorems related to right triangles.

###### Conclusion

In conclusion, Based on Pythagorean Identities Which Equation is True is a^2 + b^2 = c^2. This equation is the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This equation can be used to find the length of the sides of a triangle and prove theorems related to right triangles.

Pythagorean identities are a set of equations that are related to the Pythagorean theorem. They are used to solve problems in mathematics, especially in geometry. The equation that is true based on the Pythagorean identities is a^2 + b^2 = c^2. This equation is the Pythagorean theorem, which can be used to find the length of the sides of a triangle and prove theorems related to right triangles.

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