Question

use the formula for the cosine of the difference of two angles to find the exact value of the followin

cos (60° - 45°)

find the exact value of the expression.

cos (60° - 45°) =
(simplify your answer. type an exact answer, using radicals as needed. use integers or fractions
expression. rationalize all denominators.)

Explanation:

Step1: Recall the cosine - difference formula

The formula for \(\cos(A - B)=\cos A\cos B+\sin A\sin B\). Here \(A = 60^{\circ}\) and \(B=45^{\circ}\).

Step2: Find the values of trigonometric functions

We know that \(\cos60^{\circ}=\frac{1}{2}\), \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), and \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\).
Substitute these values into the formula:

$$
LATEXBLOCK0
$$

Step3: Simplify the expression

$$
LATEXBLOCK1
$$

Answer:

\(\frac{\sqrt{2}+\sqrt{6}}{4}\)