the minimum value of 27 tan^2 theta + 3 cot^2 theta is

Hello student,

You can use the concept of AM >= GM to solve this
take numbers as tan^2theta,tan^2theta,tan^2theta….27 times and cot^2theta,cot^2theta,cot^2theta

So we will get
[27 tan^2 theta + 3 cot^2 theta]/ 30 >= {27tan^2 theta* 3 cot^2 theta}^1/2
27 tan^2 theta + 3 cot^2 theta >= 9 * 30