Let `beta(n)=int_0^(npi)sqrt(1-sint)dt.` Find the value of `beta(2)-beta(1).`

If tan alpha = sqrt(3) and tan beta = (1)/(sqrt(3)) , then find the value of cot (alpha + beta) .

If sin(alpha+beta)=1 and sin(alpha-beta)=(1)/(2), where 0<=,beta<=(pi)/(2) ,then find the values of tan(alpha+2 beta) and tan(2 alpha+beta)

If int _(0) ^(pi) ( sin ^(3) x) e^(- sin^(2)x)dx = alpha - (beta)/( e) int _(0)^(1) sqrt(t) e^(t) " dt , then " alpha + beta is equal to _____

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))/(2)csc^(2)((1)/(2)tan^(-1)((beta)/(alpha))+(alpha^(3))/(2)sec^(2)((1)/(2)tan^(-1)((alpha)/(beta)))

If alpha and beta are the roots of the equation x^(2)-4x+1=0(alpha

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

Let alpha,beta be real number with 0<=alpha<=beta and f(x)=x^(2)-(alpha+beta)x+alpha beta such that int_(1)^(1)f(x)dx=1. Find the maximum value of int_(alpha)^( alpha)f(x)dx

Let alpha and beta be the roots of x^(2)-6x-2=0 with alpha>beta if a_(n)=alpha^(n)-beta^(n) for n>=1 then the value of (a_(10)-2a_(8))/(2a_(9))

If alpha and beta are zeroes of a quadratic polynomial ax^(2)+bx+c . Find the value of: (i) alpha^(2)-beta^(2) (ii) alpha^(3)+beta^(3) (iii) alpha^(4)beta+beta^(4)alpha (iv) sqrt((alpha)/(beta))+sqrt((beta)/(alpha)) (v) (alpha^(2))/(beta)+(beta^(2))/(alpha) (alpha^(-1)+(1)/(alpha^(-1)))(beta^(-1)+(1)/(beta^(-1)))