Question

use identities to reduce the expression to a function of α. cos(α + 180°) choose the correct function for cos(α + 180°). a. cos α b. - cos α c. sin α d. - sin α

Explanation:

Step1: Use the cosine addition formula

The cosine addition formula is \(\cos(A + B)=\cos A\cos B-\sin A\sin B\).
Here \(A = \alpha\) and \(B = 180^{\circ}\). So \(\cos(\alpha+180^{\circ})=\cos\alpha\cos180^{\circ}-\sin\alpha\sin180^{\circ}\).

Step2: Substitute the values of \(\cos180^{\circ}\) and \(\sin180^{\circ}\)

We know that \(\cos180^{\circ}=- 1\) and \(\sin180^{\circ}=0\).
Substituting these values into the above - expression:

$$
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$$

Answer:

B. \(-\cos\alpha\)