Question

find the exact value of the expression.
cos (45° - 150°)

rewrite the expression using a sum or difference formula. choose the correct answer below.
○ a. cos 45° cos 150° + sin 45° sin 150°
○ b. sin 45° cos 150° - cos 45° sin 150°
○ c. sin 45° cos 150° + cos 45° sin 150°
○ d. cos 45° cos 150° - sin 45° sin 150°

Explanation:

Step1: Recall the cosine difference formula

The formula for \(\cos(A - B)=\cos A\cos B+\sin A\sin B\). Here \(A = 45^{\circ}\) and \(B=150^{\circ}\).

Step2: Substitute \(A\) and \(B\) into the formula

Substitute \(A = 45^{\circ}\) and \(B = 150^{\circ}\) into \(\cos(A - B)=\cos A\cos B+\sin A\sin B\), we get \(\cos(45^{\circ}-150^{\circ})=\cos45^{\circ}\cos150^{\circ}+\sin45^{\circ}\sin150^{\circ}\)

Answer:

A. \(\cos45^{\circ}\cos150^{\circ}+\sin45^{\circ}\sin150^{\circ}\)