If a,b,c and k are constant quantities and `alpha, beta , gamma` are variable subjects to the relation
`a tan alpha+ b tan beta+ c tan gamma= k`, then find the minimum value of `tan^(2) alpha+tan^(2)beta+tan^(2)gamma`.

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)

If cos(alpha+beta)+sin(alpha-beta)=0 and tan beta ne1 , then find the value of tan alpha .

If alpha and beta are roots of the equation a cos theta + b sin theta = c , then find the value of tan (alpha + beta).

If alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0 , then find the value of tan^(-1) alpha - tan^(-1) beta

If alpha,beta,gamma,delta are the four solutions of the equation tan(theta+pi/4)=3 tan 3theta. No two of which have equal tangents, then the value of tan alpha+tan beta+tan gamma+tan delta=

If tan (alpha-beta)=(sin 2beta)/(3-cos 2beta) , then

Given that tan alpha = (m)/( m +1), tan beta = (1)/(2m +1) then what is the value of alpha + beta?

If 2 sin 2alpha= | tan beta+ cot beta |alpha,beta, in((pi)/(2),pi) , then the value of alpha+beta is

If a right angle be divided into three parts alpha, beta and gamma , prove that cot alpha = (tan beta + tan gamma)/(1-tan beta tan gamma) .

If atanalpha+sqrt(a^2-1)tanbeta+sqrt(a^2+1)tangamma=2a where a is a constant and alpha,beta and gamma are variable angles. Then the least value of tan^2alpha+tan^2beta+tan^2gamma is equal to