Question

If `theta_1,theta_2,theta_3` are the three values of `thetain[0,2pi]` for which `tantheta=lambda` then the value of `tan(theta_1)/3tan(theta_2)/3+tan(theta_2)/3tan(theta_3)/3+tan(theta_3)/3tan(theta_1)/3` is equal to
A. `1//3`
B. 1
C. 3
D. none of these

Answer 1

Correct Answer - C
`tan. Theta =(3tan.(theta)/(3)-"tan"^(3)(theta)/(3))/(1-3 "tan"^(2)(theta)/(3))=lambda`
`rArr tan^(3)((theta)/(3))-3lambda tan^(2)((theta)/(3))-3 tan.(theta)/(3)+lambda =0` Above equation has roots `tan.(theta_(1))/(3),tan.(theta_(2))/(3),tan.(theta_(3))/(3)`
`therefore |sumtan((theta_(1))/(3))tan((theta_(2))/(3))|=|-3|=3`