If `tan A=(alpha^2-alpha)/(alpha^2-alpha+1)` and `tanB=1/(2alpha^2-2alpha+1)` then `(A+B)` equals to

1+tan alpha*tan((alpha)/(2))

(1)/(tan3 alpha-tan alpha)-(1)/(cot3 alpha-cot alpha)=cot2 alpha

If f(alpha)=|{:(1,alpha,alpha^(2)),(alpha,alpha^(2),1),(alpha^(2),1,alpha):}| , then f(root(3)(3)) is equal to

If f(alpha) = |{:(1,alpha,alpha^2),(alpha,alpha^2,1),(alpha^2,1,alpha):}| , then find the value of f(3^(1/3)) .

If tan(alpha+beta)=2andtan (alpha-beta)=1 , then tan(2alpha) is equal to

If sin (alpha+beta)=1, sin (alpha-beta)=1/2 , then tan (alpha+ 2beta). tan (2 alpha+beta) is equal to :

If f(alpha)=[[1,alpha,alpha^2],[alpha,alpha^2,1],[alpha^2,1,alpha]] then find the value of f(3^(1/3))