Chapter 9.2, Problem 2AYU

The difference formula for cosine is $\cos \left(A-B\right)=\_\_\_\_\_\_$. (p.490)

To determine

To fill: The difference formula for $\text{cos}\left(A - B\right)$.

Answer to Problem 2AYU

Solution:

The required formula is $\text{cos} \left(A - B\right) = \text{cos}A\text{ cos}B + \text{sin}A \text{sin}B$.

Given:

It is asked to fill in the difference of cosine formula.

Explanation of Solution

Difference formula for the cosine function:

$\begin{array}{}\text{cos} \left(\alpha - \beta \right) = \text{cos}\alpha \text{cos}\beta + \text{sin}\alpha \text{sin}\beta \end{array}$

By the cosine difference formula, $\text{cos}\left(A - B\right)$ can be written as follows:

$\text{cos}\left(A - B\right) = \text{cos}A \text{cos}B + \text{sin}A \text{sin}B$