Proving Inequality: Vector Method for Cos2A+Cos2B+Cos2C in Triangle ABC

[utkarshakash]

Homework Statement

In a triangle ABC, prove by vector method cos2A+cos2B+cos2C≥ -3/2.

Homework Equations

The Attempt at a Solution

I can change the LHS of the inequality to the form
(cos2A i + cos2B j + cos2C k).(i+j+k)

 

[tiny-tim]

hi utkarshakash!

hint: 2A + 2B + 2C = 360° …

so draw a circle! ​