[x+y,y+z,z+x],[z,x,y],[1,1,1]

Prove that abs[[1,x,x^2],[1,y,y^2],[1,z,z^2]]=(x-y)(y-z)(z-x)

|[x,1,y+z],[y,1,z+x],[z,1,x+y]|=

The value of |[[1,x,y+z],[1,y,z+x],[1,z,x+y]]| is

Find the value of : |(1+x,y,z),(x,1+y,z),(x,y,1+z)|

If x, y, z being positive |[1, log _x y,log _x z],[log _y x,1,log _y z],[log _z x,log _z y, 1]|=

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n x^2+y^2+z^2+2x y z=1 2(sin^(-1)x+sin^(-1)y+sin^(-1)z)=cos^(-1)x+cos^(-1)y+cos^(-1)z x y+y z+z x=x+y+z-1 (x+1/x)+(y+1/y)+(z+1/z)geq6

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi,t h e n x^2+y^2+z^2+2x y z=1 2(sin^(-1)x+sin^(-1)y+sin^(-1)z)=cos^(-1)x+cos^(-1)y+cos^(-1)z x y+y z+z x=x+y+z-1 (x+1/x)+(y+1/y)+(z+1/z)geq6

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1). x y+y z+z y and (2). x(y+z)+y(z+x)+z(x+y)

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z y and (2) x(y+z)+y(z+x)+z(x+y)

If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then find the values of (1) x y+y z+z x and (2) x(y+z)+y(z+x)+z(x+y)