Let `alpha,beta` be the distinct positive roots of the equation `tanx=2x` then evaluate `int_0^1 sin alpha x .sin betax dx` independent of `alpha and beta`

Let alpha & beta be distinct positive roots of the equation tanx = 2x , then evaluate int_(0)^(1)sin(alphax).sin(betax) dx

Let alpha, beta are the roots of the equation x^(2)+x+1=0 , then alpha^3-beta^3

If alpha, beta in C are distinct roots of the equation x^2+1=0 then alpha^(101)+beta^(107) is equal to

If alpha, beta in C are distinct roots of the equation x^2-x+1=0 then alpha^(101)+beta^(107) is equal to

If alpha,beta in C are distinct roots of the equation x^(2)+1=0 then alpha^(101)+beta^(107) is equal to

If alpha, beta in C are the distinct roots of the equation x^(2)-x+1=0 , then alpha^(101)+beta^(107) is equal to

If alpha , beta in C are the distinct roots of the equation x^2-x+1 = 0 , then (alpha)^101+(beta)^107 is equal to

int 2 sin (alpha-beta) x sin (alpha+beta) x dx

If tan alpha and tan beta are the roots of the equation x^(2) +px + q = 0 , then the value of sin^(2) (alpha +beta) + p cos (alpha + beta) sin (alpha + beta) + q cos^(2) (alpha + beta) is