Trigonometry is one of the funny subcategories of mathematics.it is very useful in engineering and scientific research. Some people think it is very easy and some people think that is a tough subject. The toughness of Trigonometry depends that what is your basics knowledge of trigonometry. Now here we look for a very important formula of trigonometry and its relation with other trigonometrical identities.

## Derivation of Cos2x Formula?

### The relation between Co2x and Sinx only

Sin^{2}x +Cos^{2}x = 1

Cos^{2}x = 1 - Sin^{2}x

On putting the value of Cos^{2}x in equation (1)

Cos2x = 1 - Sin^{2}x
- Sin^{2}x

**Cos2x = 1 - 2 Sin ^{2}x**

**After Rearranging **

**2 Sin ^{2}x = 1 - **

**Cos2x**

it is another relation of Cos2x with Sinx

### Relation of Co2x With Cosx

Sin^{2}x +Cos^{2}x = 1

Sin^{2}x = 1 - Cos^{2}x

On putting this value in equation (1)

Cos2x = Cos^{2}x - (1 - Cos^{2}x )

**Cos2x = 2Cos ^{2}x - 1 **

On Rearranging

**2Cos ^{2}x = **

**Cos2x + 1**

**it is proved.Cos2x formula is also lnown as double angle formula.**