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 show that x^3+y^3+z^3=3x y z .

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

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

Prove that sin (x + y ) sin (x -y) + sin ( y+ z) sin (y - z) + sin (z+x) sin (z-x) = 0.

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)

Prove that : |{:(1,x,yz),(1,y,zx),(1,z,xy):}|=(x-y)(y-z)(z-x)

show that |[y+z ,x, y],[ z+x, z, x],[x+y, y ,z]|=(x+y+z)(x-z)^2

If tan - A tan B = x, cot B - cot A = y prove that cot (A - B) = (1)/(x) + (1)/(y)

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