# What trig identity did they use?

• quickclick330
In summary, a trigonometric identity is a mathematical equation that relates different trigonometric functions of an angle. They are important because they allow us to manipulate and solve equations involving trigonometric functions, and provide a deeper understanding of these functions. To prove a trig identity, algebraic manipulations and definitions of trigonometric functions are used. An example of a commonly used trig identity is the Pythagorean identity, sin²θ + cos²θ = 1. A list of all trig identities can be found online or in the appendix of most trigonometry textbooks.
quickclick330
Hi I'm having trouble understanding how they simplified this integration using trig substitutions...I really don't know what identities they used to make these substitutions or the strategy behind why this substitution was made(particularly the 3 steps in the red box). Obviously it works but I just can't click into place why...thanks for the help!

double angle formula, sin(2x) = 2sinxcosx

## 1. What is a trig identity?

A trigonometric identity is a mathematical equation that relates different trigonometric functions of an angle. These identities are used to simplify expressions and solve equations involving trigonometric functions.

## 2. Why are trig identities important?

Trig identities are important because they allow us to manipulate and solve equations involving trigonometric functions. They also provide a deeper understanding of the relationships between different trigonometric functions.

## 3. How do you prove a trig identity?

To prove a trig identity, you need to use algebraic manipulations and the definitions of trigonometric functions. You can also use known trig identities and basic algebraic principles to transform one side of the equation into the other.

## 4. Can you give an example of a commonly used trig identity?

One commonly used trig identity is the Pythagorean identity, which states that sin²θ + cos²θ = 1. This identity is used in many trigonometric calculations and can also be used to prove other identities.

## 5. Where can I find a list of all trig identities?

There are many resources available online that provide a comprehensive list of trigonometric identities, such as math textbooks, math websites, and online math forums. You can also find a list of trig identities in the appendix of most trigonometry textbooks.

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