To find [tex]\(\cos(x + y)\)[/tex], we use the angle addition formula for cosine, which is a well-known trigonometric identity. Let's break down the steps:
1. Understand the Angle Addition Formula:
The angle addition formula for cosine states that:
[tex]\[
\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)
\][/tex]
2. Apply the Formula:
We need to apply this formula directly to our expression [tex]\(\cos(x + y)\)[/tex].
3. Write the Final Expression:
By substituting [tex]\(x\)[/tex] and [tex]\(y\)[/tex] into the angle addition formula, we get:
[tex]\[
\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)
\][/tex]
Therefore, the formula for [tex]\(\cos(x + y)\)[/tex] is:
[tex]\[
\cos(x + y) = \cos(x) \cos(y) - \sin(x) \sin(y)
\][/tex]
This identity allows us to express the cosine of the sum of two angles in terms of the sines and cosines of the individual angles.
