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° find the exact value of the expression. cos (45° - 150°) = (simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression. rationalize all denominators.)

Explanation:

Step1: Use the cosine difference formula

The formula for \(\cos(A - B)=\cos A\cos B+\sin A\sin B\). Here \(A = 45^{\circ}\) and \(B=150^{\circ}\), so \(\cos(45^{\circ}-150^{\circ})=\cos45^{\circ}\cos150^{\circ}+\sin45^{\circ}\sin150^{\circ}\)

Step2: Find the values of trigonometric functions

We know that \(\cos45^{\circ}=\frac{\sqrt{2}}{2}\), \(\cos150^{\circ}=-\frac{\sqrt{3}}{2}\), \(\sin45^{\circ}=\frac{\sqrt{2}}{2}\), \(\sin150^{\circ}=\frac{1}{2}\)

Substitute these values into the formula:

$$
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$$

Answer:

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