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Cos2x Formula - Trigonometry Double Angle Formula

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?

As we know that 
Cos(A+B) = CosA CosB - SinA SinB -----(1)

Then from equation (1)

Cos(x+x) = Cosx.Cosx - Sinx Sinx

it is one of the best results of Cos2x with Sinx. Let's say equation (2)

The relation between Co2x and Sinx only

As We know that 

Sin2x +Cos2x = 1

Cos2x = 1 - Sin2x

On putting the value of Cos2x in equation (1)

Cos2x = 1 - Sin2x  - Sin2x

Cos2x = 1 - 2 Sin2x

After Rearranging 

2 Sin2x =  1 - Cos2x 

it is another relation of Cos2x with Sinx

Relation of Co2x With Cosx

Sin2x +Cos2x = 1

Sin2x = 1 - Cos2x  

On putting this value in equation (1)

Cos2x = Cos2x  - (1 - Cos2)

Cos2x  = 2Cos2x  -

On Rearranging

2Cos2x  = Cos2x + 1

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

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