If `x=asecthetacosphi` ,`y=secthetasinphiandz=ctantheta`,show that`(x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(c^(2))=1`.

Let a,b,c be the real numbers.The following system of equations in x,y, and z(x^(2))/(a^(2))+(y^(2))/(b^(2))-(z^(2))/(a^(2))=1,(x^(2))/(a^(2))-(y^(2))/(b^(2))+(z^(2))/(a^(2))=1,-(x^(2))/(a^(2))+(y^(2))/(b^(2))+(z^(2))/(a^(2))=1 has a.no solution b.unique solution c .infinitely many solutions d.finitely many solutions

a(y+z)=x,b(z+x)=y,c(x+y)=z prove that (x^(2))/(a(1-bc))=(y^(2))/(b(1-ca))=(z^(2))/(c(1-ab))

If a^(x)=b^(y)=c^(z) and abc=1, then find ((x^(2))/(x^(2)-zy)+(y^(2))/(y^(2)-zx)+(z^(2))/(z^(2)-xy))

If a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]

Show that: ((a^(x+1))/(a^(y+1)))^(x+y)((a^(y+2))/(a^(z+2)))^(y+z)((a^(z+3))/(a^(x+3)))^(z+x)=1

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

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

If xy+yz+zx=1 show 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=xyz then show that (2x)/(1-x^(2))+(2y)/(1-y^(2))+(2z)/(1-z^(2))=(8xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))