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,
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:
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
1. Express 2 Cos 7x Cos 3y as a Sum
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
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.