If a, b, c and k are real constants and `alpha, beta, gamma` are variables subject to the condition that `a tanalpha + btanbeta+ c tangamma=k` , then prove using vectors that `tan^2 alpha + tan^2 beta+ tan^2gamma>= k^2 /(a^2 + b^2 + c^2)`

Answer

Minimum value is `((k^(2))/(a^(2)+b^(2)+c^(2)))`