`alpha=pi/4020` and `beta=2009/4020pi` and `int_alpha^beta dx/(1+tanx)=(kpi)/8040`, then `k` is equal to …..

int _(alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

If alpha and beta be between 0 and (pi)/(2)and if cos(alpha+beta)=(12)/(13) and sin(alpha-beta)=3/5, then sin 2 alpha is equal to

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

If alpha+beta=pi/2a n dbeta+gamma=alpha, then tanalpha equals

If sin alpha = 3/5, tan beta = 1/2 and pi/2 lt alpha lt pi lt beta lt (3pi)/2 , show that 8 tan alpha - sqrt(5) sec beta = - 7/2 .

If sin^(4)alpha+cos^(4)beta+2=4 sin alpha cos beta, 0 le alpha, (pi)/(2) , then (sin alpha+cos beta) is equal to

If cos( alpha+beta) + sin(alpha-beta) = 0 and 2010tan beta - 1 = 0 then tan alpha is equal to

Given alpha and beta are the roots of the quadratic equation x^(2)-4x+k=0(kne0). If alpha beta, alpha beta^(2)+alpha^(2)beta and alpha^(3)+beta^(3) are in geometric progression, then the value of k is equal to

If cos(alpha+beta)=4/5; sin(alpha-beta)=5/13 and alpha,beta lie between 0&pi/4 then find the value of tan2alpha

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/2) is equal to-