If the sum of solution of the equation `2^(sin^2 x) + 5. 2^(cos^2 x) = 7` where `x in (0,2pi)` is equal to `kpi (k in I),`then the value of `tan^-1(k – 1) + tan^-1(k)+tan^-1(k+ 1)` is equal to

If the number of principal solutions of the equation tan(7pi cos x)=cot(7pi sin x) is k, then (k)/(5) is equal to

If tan x-tan^(2)x=1, then the value of tan^(4)x-2tan^(3)x-tan^(2)x+2tan x+k=4, then k is equal to

sum _(k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

sum _(k=1)^(n) tan^(-1). 1/(1+k+k^(2)) is equal to

If 2 tan^(-1)x= sin^(-1)K then the value of k is

If 2 tan ^(-1) x = sin ^(-1) k then the value of k is -

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 :

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 :