If the equation `x^3+b x^2+c x+1=0,(bltc),` has only one real root `alpha` , then the value of `2tan^(-1)(cosec alpha)+tan^(-1)(2 sinalpha sec^2alpha)` is

If the equation x^3+b x^2+c x+1=0,(b

If alpha in (-(pi)/(2), 0) , then find the value of tan^(-1) (cot alpha) - cot^(-1) (tan alpha)

The value of the integral int_(0)^(3alpha) cosec (x-alpha)cosec(x-2alpha)dx is

If alpha is a non-real fifth root of unity, then the value of 3^(|1+alpha+alpha^(2),alpha^(-2)-alpha^(-1)| , is

If alpha is the only real root of the equation x^3 + bx^2 + cx + 1 = 0 (b < c) , then the value of tan^-1 alpha+ tan^-1 (alpha^-1) is equal to :

If alpha " and " beta ( alpha gt beta) are roots of the equation x^(2) - sqrt2 x + sqrt( 3 - 2 sqrt 2 ) = 0", then the value of " ( cos^(-1) alpha + tan^(-1) alpha + tan ^(-1) beta) is equal to

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 alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0 , then find the value of tan^(-1) alpha - tan^(-1) beta

If alpha and beta are roots of the equation 2x^(2)-3x-5=0 , then the value of (1)/(alpha)+(1)/(beta) is

If alpha and beta are roots of the equation x^(2)-2x+1=0 , then the value of (alpha)/(beta)+(beta)/(alpha) is