Final answer:
Using the trigonometric identity cos(A + B) = cos A cos B - sin A sin B, we can simplify the expression cos A + cos(120⁰ + A) + cos(120⁰ - A) is equal to 0.
Step-by-step explanation:
We can use the trigonometric identity cos(A + B) = cos A cos B - sin A sin B to rewrite the equation:
cos A + cos(120⁰ + A) + cos(120⁰ - A)
= cos A + [cos 120⁰ cos A - sin 120⁰ sin A] + [cos 120⁰ cos A + sin 120⁰ sin A]
= cos A + cos 120⁰ cos A + cos 120⁰ cos A - sin 120⁰ sin A + sin 120⁰ sin A
= cos A + 2 cos 120⁰ cos A
= cos A - cos A
= 0
Therefore, cos A + cos(120⁰ + A) + cos(120⁰ - A) = 0.