If x,y,z are in A.P., prove that `(x+2y-z)(z+2y-x)(x+z-y) = 4xyz`

If a,b,c are in A.P. and x,y,z are in G.P., then show that x^(b-c).y(c-a).z(a-b)=1 .

If xy + yz + zx = 1 , prove that : x/(1-x^2)+y/(1-y^2)+z/(1-z^2)= (4xyz)/((1-x^2)(1-y^2)(1-z^2)) .

If x, y, z are in A.P. and tan^(-1) x, tan^(-1) y and tan^(-1)z are also in A.P. then show that x=y=z and y≠0

If (x(y+z-x))/log x = (y(z+x-y))/log y = (z(x+y-z))/log z ," prove that "x^(y) y^(x) = z^(y) y^(z) = x^(z) z^(x) .

If cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that x^(2) + y^(2) + z^(2) + 2xyz = 1

If x,y,z are positive real numbers, prove that: sqrt(x^-1 y).sqrt(y^-1z).sqrt(z^(-1)x)=1

If x +y+ z=xyz , prove that : (2x)/(1-x^2)+(2y)/(1-y^2)+(2z)/(1-z^2)= (2x)/(1-x^2). (2y)/ (1-y^2). (2z)/(1-z^2) .

If x, 2y, 3z are in A.P where distinct numbers x,y,z are in GP then the common ratio of the G.P. is

If x +y+ z=xyz , prove that : (3x-x^3)/(1-3x^2)+ (3y-y^3)/(1-3y^2)+(3z-z^3)/(1-3z^2)= (3x-x^3)/(1-3x^2). (3y-y^3)/(1-3y^2).(3z-z^3)/(1-3z^2) .