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

Consider three points : P (- sin (beta- alpha), - cos beta), Q = (cos(beta-alpha), sin beta), and R = (cos (beta - alpha + theta), sin (beta - theta)) , where 0< alpha, beta, theta < pi/4 Then

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

If tan (alpha- beta)= (sin 2 beta)/(5-cos 2 beta) , find tan alpha: tan beta .

Evaluate int_(0)^(pi)(x dx)/(1+cos alpha sin x) ,where 0lt alpha lt pi .

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

If 2 tan beta+cot beta= tan alpha , prove that cot beta= 2 tan (alpha-beta) .

If a tan alpha+b tan beta=(a+b) tan ((alpha+beta)/2) , where alpha ne beta , prove that : a cos beta= b cos alpha .

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

If 2 sin alphacos beta sin gamma=sinbeta sin(alpha+gamma),then tan alpha,tan beta and tan gamma are in

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