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.

FAQs (Frequently Asked Questions)

1. What is a Cosine Function?

Ans. The cosine function is one of the most important functions in trigonometry. In a right-angled triangle, the cosine function is defined as the ratio of the length of the base to the length of the hypotenuse side.

2. What is the Use of the Cos A Cos B Formula?

Ans. The Cos A Cos B formula is used in solving the integration problems.

3. How the Cos A Cos B Formula is Derived?

Ans. The formula of Cos A Cos B is derived from the sum and difference identities for cosine.