If the roots of the equation `x^(3) -10 x + 11 = 0` are u, v, and w, then the value of `3 cosec^(2) (tan^(-1) u + tan^(-1) v + tan^(-1 w)` is ____

If the roots of the equation x^(3)-10x+11=0 are u, v, and w, then the value of 3cosec^(2)(tan^(-1)u+tan^(-1)v+tan^(-1)w) is

If tan alpha, tan beta, tan lambda are the roots of the equation x^(3) - px^(2) - r = 0 then the value of (1+tan^(2) alpha) (1+tan^(2) beta)(1+tan^(2)lambda) =

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

The value of 2tan^(-1)(cosec(tan^(-1)x)-tan(cot^(-1)x)) is equal to

Prove that 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x (x != 0)

Prove that: tan^(-1)(x)=2tan^(-1)(cosec tan^(-1)x-tan cot^(-1)x)

The number of values of x satisfying the equation tan^(-1)(x+1)+tan^(-1)x+tan^(-1)(x-1)=tan^(-1)3x is ____