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

If 0 lt alpha lt beta lt (pi)/(2) then

Minimum value of (sec^4alpha)/(tan^2beta)+(sec^4beta)/(tan^2alpha), where alpha!=pi/2,beta!=pi/2 ,0

The value of int_(alpha)^(beta) x|x|dx , where a lt 0 lt beta , is

(1+tan alpha tan beta)^2 + (tan alpha - tan beta)^2 =

Simplify be reducing to a single term : (tan alpha - tan ( alpha - beta))/(1 + tan alpha tan ( alpha - beta))

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is

The value of the integral int_alpha^beta (1)/(sqrt((x-alpha)(beta-x)))dx " for "beta gt alpha , is

Let alpha, beta are the roots of the equation x^(2)+7x+k(k-3)=0 , where k in (0, 3) and k is a constant. Then the value of tan^(-1)alpha+tan^(-1)beta+"tan"^(-1)(1)/(alpha)+"tan"^(-1)(1)/(beta) is :

If tan alpha=(1+2^(-x))^(-1), tan beta=(1+2^(x+1))^(-1) then alpha+beta equals

If tan alpha =m/(m+1) and tan beta =1/(2m+1) , then alpha+beta is equal to