thevenin and norton theorem solved problems -Electricaldiary

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)

 if A = B = x

Then from equation (1)

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

Cos2x = Cos²x – Sin²x --------(2)

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 - Cos²x )

Cos2x  = 2Cos²x  - 1 

On Rearranging

2Cos²x  = Cos2x + 1

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