Question

in the following problem, the expression is the right side of the formula for $\cos(\alpha - \beta)$ with $\cos(89^{\circ})\cos(44^{\circ})+\sin(89^{\circ})\sin(44^{\circ})$ a. identify $\alpha$ and $\beta$ in each expression. the value for $\alpha$: $89^{\circ}$ the value for $\beta$: $44^{\circ}$ b. write the expression as the cosine of an angle. $\cos45^{\circ}$ c. find the exact value of the expression. (type an exact answer, using fraction, radicals and a rationalized denominator.)

Explanation:

Step1: Use the formula from part b

From part b, the expression is \(\cos(45^{\circ})\).

Step2: Recall the exact value of \(\cos(45^{\circ})\)

We know that \(\cos(45^{\circ})=\frac{\sqrt{2}}{2}\).

Answer:

\(\frac{\sqrt{2}}{2}\)