# Double-angle identities

##### Examples

###### Free to Join!

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

## Using double angle identities in trigonometry

Identities in math shows us equations that are always true. There are many trigonometric identities (Download the Trigonometry identities chart here ), but today we will be focusing on double angle identities, which are named due to the fact that they involve trig functions of double angles such as sin$\theta$, cos2$\theta$, and tan2$\theta$. It's hard to simplify complex trigonometric functions without these formulas.

How to use double angle identities Firstly, what are double angle identities? Let's take a look at the trigonometry identity chart here:

For now, let's take a look at some double angle identities examples. Using the above trig identities cheat sheet, we can go through this trigonometric identities tutorial:

If you look at the trigonometry identity chart, you won't find a number, followed by sine, then cosine—not in quotient identities, not in reciprocal identities, not in Pythagorean identities, and not in sum and difference identities.

For both formulas we have a sine, cosine, which is nice. But the number in front is of our problems is 14, whereas in the double angle identity, the number in front is 2. What should be our next step? Multiply the whole expression by 7. That will give us 7(sin2$\theta$). Multiplying this into the right side of the equation, we will get:

Let ? = 6x, which gives us:

Formulas:$\sin 2\theta = 2\sin x\cos x$

$\cos 2 \theta = {\cos ^2}x - {\sin^2}x$

$= \;2{ \cos ^2}x - 1$

$= \;1 - 2{\sin ^2}x$

$\tan 2 \theta = {{2\tan x} \over {1 - \tan ^2}x}$

###### Basic Concepts

###### Related Concepts

remaining today

remaining today