Which expression is equivalent to cos120°? ° cos240° cos300° cos420°?

Answer:Option 1 - cos 240°Step-by-step explanation:Given : Expression [tex]\cos 120^\circ[/tex]To find : Which expression is equivalent to given expression ?   Solution : The given  expression is equivalent to those whose value is same as [tex]\cos 120^\circ[/tex]Value of [tex]\cos 120^\circ= \cos (180-60)[/tex] [tex]\cos 120^\circ= -\cos 60[/tex] [tex]\cos 120^\circ= -\frac{1}{2}[/tex]value of cos in second quadrant is negative.Option 1 : [tex]\cos 240^\circ[/tex][tex]\cos 240^\circ= \cos (180+60)[/tex] [tex]\cos 240^\circ= -\cos 60[/tex] [tex]\cos 240^\circ= -\frac{1}{2}[/tex]EquivalentOption 2 : [tex]\cos 300^\circ[/tex][tex]\cos 300^\circ= \cos (360-60)[/tex] [tex]\cos 300^\circ= \cos (2\times 180- 60)[/tex] [tex]\cos 300^\circ= \cos (60)[/tex] [tex]\cos 300^\circ= \frac{1}{2}[/tex]Not equivalent Option 3 : [tex]\cos 420^\circ[/tex][tex]\cos 420^\circ= \cos (360+60)[/tex] [tex]\cos 300^\circ= \cos (2\times 180+60)[/tex] [tex]\cos 420^\circ= \cos 60[/tex] [tex]\cos 420^\circ= \frac{1}{2}[/tex]Not equivalentTherefore, Correct option is 1.[tex]\cos 120^\circ=\cos 240^\circ=-\frac{1}{2}[/tex]