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.\n\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°

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.\n\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°

Answer

Explanation:

Step1: Recall the cosine of difference formula

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

Step2: Substitute values into the formula

Substituting (A = 60^{\circ}) and (B = 45^{\circ}) into (\cos(A - B)=\cos A\cos B+\sin A\sin B), we get (\cos(60^{\circ}-45^{\circ})=\cos60^{\circ}\cos45^{\circ}+\sin60^{\circ}\sin45^{\circ})

Answer:

D. (\cos 60^{\circ}\cos 45^{\circ}+\sin 60^{\circ}\sin 45^{\circ})