use identities to reduce the expression to a function of α. cos(α + 180°) choose the correct function for…

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

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

Answer

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: [ \begin{align*} \cos(\alpha + 180^{\circ})&=\cos\alpha\times(-1)-\sin\alpha\times0\ &=-\cos\alpha-0 \end{align*} ]

Answer:

B. (-\cos\alpha)