. If `tan^2 pi(x+y)+cot^2pi (x+y)=1+sqrt(2x)/(1+x^2)` where `x,y in RR` then the least positive value of y is

If tan^(2) {pi(x+y)}+cot^(2) {pi (x+y)}=1+sqrt((2x)/(1+x^(2))) where x, y in R , then find the least possible value of y.

If the sum of all value of x satisfying the system of equations tan x + tan y+ tan x* tan y=5 sin (x +y)=4 cos x * cos y is (k pi )/2 , where x in (0, (pi)/(2)) then find the values of k .

If x, y in [0, 2pi] and sin x + sin y=2 , then the value of x+y is

If the expression sqrt(log^2x)+sqrt(4 cos^2 y-4 cos y+1) takes its least value , then value of x+y is greater than, (where x,y gt0 )

if (1- tan x)/(1+tan x) = tan y and x -y = pi/6, then x,y are respectively

If x and y are positive real numbers such that x^(2)y^(3)=32 then the least value of 2x+3y is

If tan^-1(1/y)=-pi+cot^-1 y, where y=x^2-3x+2, then find the value of x

Let x+(1)/(x)=2, y+(1)/(y)=-2 and sin^(-1)x+cos^(-1)y=m pi , then the value of m is

If tan^(-1)x+tan^(-1)y=pi/4, then write the value of x+y+x ydot

If tan^(-1)x+tan^(-1)y=pi/4, then write the value of x+y+x ydot