Let `t_1,t_2,t_3` be the three distinct points on circle |t|=1. if `theta_1,theta_2` and `theta_3` be the arguments of `t_1,t_2,t_3` respectively then `cos(theta_1- theta_2) + cos (theta_2-theta_3)+ cos (theta_3-theta_1)`

Options

A. `ge-3/2`
B. `le -3/2`
C. `ge 3/2`
D. none of these

Answer

A

Explanation

We have `|z_(1)|=|z_(2)|=|z_(3)|=1`
Now, `|z_(1)+z_(2)+z_(3)| le 0`
`rArr |z_(1)|^(2)+|z_(2)|^(2)+|z_(3)|^(2)+2 "Re"(z_(1)barz_(2)+z_(2)barz_(3)+z_(3)barz_(1)) ge 0`
`=rArr 3+2 {cos(theta_(1)-theta_(2))+cos(theta_(2)-theta_(3))+cos(theta_(3)-theta_(1))} ge 0`
`rArr cos(theta_(1)-theta_(2))+cos(theta_(3)-theta_(1)) ge -3/2`