If `x+y+z=0`, show that :` cot(x+y-z) cot (z+x-y) +(cot(x+y-z) cot (y+z-x)+cot(y+z-x) cot (z+x-y)=1`

If x+y+z=0 then cot(x+z-y),cot(x+y-z)+cot(x+y-z),cot(y+z-x)+cot(y+z-x)*cot(z+x-y)=

Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

If x>y>z>0, then find the value of cot^(-1)(xy+1)/(x-y)+cot^(-1)(yz+1)/(zy-z)+cot^(-1)(zx+1)/(z-x)

If cot^(-1)x + cot^(-1)y + cot^(-1)z = pi , prove that xy + yz + zx = 1 .

If x + y = 2z then (x)/(x-z) +(z)/(y-z) = ?

If x gt y gt z gt 0 , then find the value of "cot"^(-1) (xy + 1)/(x - y) + "cot"^(-1)(yz + 1)/(y - z) + "cot"^(-1)(zx + 1)/(z - x)

If cot^(2)x=cot(x-y)*cot(x-z) , then cot2x is equal to (x!= pm pi/4)

Determinant (x-y)(y-z)(z-x)(x+y+z)