# 2 Cos A Cos B Formula

## Formula of 2 Cos A Cos B

2 Cos A Cos B is the product to sum trigonometric formulas that are used to rewrite the product of cosines into sum or difference. The 2 cos A cos B formula can help solve integration formulas involving the product of trigonometric ratio such as cosine. The formula of 2 Cos A Cos B can also be very helpful in simplifying the trigonometric expression by considering the product term such as Cos A Cos B and converting it into sum.

Here, we will look at the 2 Cos A Cos B formula and how to derive the formula of 2 Cos A Cos B.

### 2 Cos A Cos B Formula Derivation

The 2 Cos A Cos B formula can be derived by observing the sum and difference formula for cosine.

As we know,

• Cos ( A + B ) = Cos A Cos B - Sin A Sin B...   (1)

• Cos ( A- B ) = Cos A Cos B + Sin A Sin B…….(2)

Adding the equation (1) and (2), we get

Cos (A + B) + Cos (A - B) = Cos A Cos B - Sin A Sin B + Cos A Cos B + Sin A Sin B

Cos (A + B) + Cos (A - B)  = 2 Cos A Cos B (The term Sin A Sin B is cancelled due to the opposite sign).

Therefore, the formula of 2 Cos A Cos B is given as:

 2 Cos A Cos B = Cos (A + B) + Cos (A - B)

In the above 2 Cos A Cos B formula, the left-hand side is the product of cosine whereas the right-hand side is the sum of the cosine.

### 2 Cos A Cos B Formula Application

Express 2 Cos 7x Cos 3y as a Sum

Solution:

Let A = 7x and B = 3y

Using the formula:

2 Cos A Cos B = Cos (A + B) + Cos (A - B)

Substituting the values of A and B in the above formula, we get

2 Cos A Cos B = Cos (7x + 3y) + Cos (7x - 3y)

2 Cos A Cos B = Cos 10x + Cos 4y

Hence, 2 Cos 7x Cos 3y = Cos 10x + Cos 4y

### Conclusion

This article discusses 2 Cos A Cos B formulas, The Cos A Cos B is a formula that is derived using the sum and difference trigonometric identity for cosine. The formula is widely used in solving integration problems.