which expression is equivalent to cos120°?\ncos60°\ncos240°\ncos300°\ncos420°

Explanation:

Step1: Calculate the value of $\cos120^{\circ}$

Using the formula $\cos(180^{\circ}-\alpha)=-\cos\alpha$, for $\alpha = 60^{\circ}$, we have $\cos120^{\circ}=\cos(180^{\circ} - 60^{\circ})=-\cos60^{\circ}=-\frac{1}{2}$.

Step2: Calculate the value of $\cos240^{\circ}$

Using the formula $\cos(180^{\circ}+\alpha)=-\cos\alpha$, for $\alpha = 60^{\circ}$, we have $\cos240^{\circ}=\cos(180^{\circ}+ 60^{\circ})=-\cos60^{\circ}=-\frac{1}{2}$.

Step3: Calculate the value of $\cos300^{\circ}$

Using the formula $\cos(360^{\circ}-\alpha)=\cos\alpha$, for $\alpha = 60^{\circ}$, we have $\cos300^{\circ}=\cos(360^{\circ}- 60^{\circ})=\cos60^{\circ}=\frac{1}{2}$.

Step4: Calculate the value of $\cos420^{\circ}$

Using the formula $\cos(\alpha + 360^{\circ})=\cos\alpha$, for $\alpha = 60^{\circ}$, we have $\cos420^{\circ}=\cos(360^{\circ}+ 60^{\circ})=\cos60^{\circ}=\frac{1}{2}$.

Answer:

$\cos240^{\circ}$