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

use the formula for the cosine of the difference of two angles to find the exact value of the following expression. \ncos (60° - 45°)\n\nrewrite the expression using a sum or difference formula. choose the correct answer below. \na. sin 60° cos 60° + cos 45° sin 45°\nb. sin 60° cos 45° - cos 60° sin 45°\nc. cos 60° cos 45° - sin 60° sin 45°\nd. cos 60° cos 45° + sin 60° sin 45°\n\nfind the exact value of the expression. \ncos (60° - 45°) = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

use the formula for the cosine of the difference of two angles to find the exact value of the following expression. \ncos (60° - 45°)\n\nrewrite the expression using a sum or difference formula. choose the correct answer below. \na. sin 60° cos 60° + cos 45° sin 45°\nb. sin 60° cos 45° - cos 60° sin 45°\nc. cos 60° cos 45° - sin 60° sin 45°\nd. cos 60° cos 45° + sin 60° sin 45°\n\nfind the exact value of the expression. \ncos (60° - 45°) = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Answer

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}), so (\cos(60^{\circ}-45^{\circ})=\cos60^{\circ}\cos45^{\circ}+\sin60^{\circ}\sin45^{\circ})

Step2: Substitute 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:

[ \begin{align*} \cos(60^{\circ}-45^{\circ})&=\frac{1}{2}\times\frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}\times\frac{\sqrt{2}}{2}\ &=\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4}\ &=\frac{\sqrt{2}+\sqrt{6}}{4} \end{align*} ]

Answer:

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