The maximum possible integral value of `(beta-alpha)/(tan^(-1)beta - tan^(-1)alpha`, where `0lt alpha lt beta lt sqrt3`, is

If alpha+beta=(pi)/(4) , then the value of (1+tanalpha)(1+tanbeta) is

Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (alpha+nbeta) .

If (1)/(cos alpha * cos beta )+ tan alpha * tan beta = tan gamma , where 0 lt gamma lt (pi)/2 and alpha , beta are positive acute angles , show that (pi)/4 lt gamma lt (pi)/2

Let -pi/6 beta_1 and alpha_2 >beta_2 , then alpha_1 + beta_2 equals

If cot (alpha + beta )=0 , then sin(alpha+2beta ) =

The point of intersection of lines is (alpha, beta) , then the equation whose roots are alpha, beta , is

If alpha and beta are the roots of the equation x^2-4x + 1=0(alpha > beta) then find the value of f(alpha,beta)=(beta^3)/2csc^2(1/2tan^(- 1)(beta/alpha))+(alpha^3)/2sec^2(1/2tan^- 1(alpha/beta))

Check the following relations R and rho for reflexive, symmetry and transitivity. alpha rho beta iff alpha is perpendicular to beta , where alpha and beta are straight lines in a plane.