1. The problem statement, all variables and given/known data If a,b,c and k are real constants and α,β,γ are variables subject to the condition that atanα+btanβ+ctanγ = k, then prove using vectors that tan^2 α+tan^2 β+ tan^2 γ ≥ k^2/(a^2+b^2+c^2) 2. Relevant equations 3. The attempt at a solution [itex](ai+bj+ck).(tan \alpha i+ tan \beta j+ tan \gamma k) = k \\ k^2 = (a^2+b^2+c^2)(tan^2 \alpha + tan^2 \beta + tan^2 \gamma)[/itex] But what I arrive at is an equation instead of the inequality required to prove.