Question

use a sum or difference formula to find the exact value of cos 15°
find the exact value of the expression.
cos 15° = □
(simplify your answer. type an exact answer, using

Explanation:

Step1: Express \(15^{\circ}\) as a difference

We know that \(15^{\circ}=45^{\circ}-30^{\circ}\).

Step2: Use the cosine - difference formula

The cosine - difference formula is \(\cos(A - B)=\cos A\cos B+\sin A\sin B\).
Here \(A = 45^{\circ}\) and \(B=30^{\circ}\).
We know that \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\), and \(\sin30^{\circ}=\frac{1}{2}\).
Substitute these values into the formula:

$$
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$$

Answer:

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