If `(y/z)^a (z/x)^b (x/y)^c=1`, then prove that `(y/z)^((1)/(b-c))=(z/x)^((1)/(c-a))=(x/y)^((1)/(a-b))`.

If |(a,y,z),(x,b,z),(x,y,c)|=0 , then prove that (a)/(a-x)+(b)/(b-y)+(c)/(c-z)=2

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)

If a/(y+z) = b/(z + x) = c/(x+y) , then prove that (a(b-c))/(y^(2)-z^(2)) = (b(c-a))/(z^(2)-x^(2)) = (c(a-b))/(x^(2)-y^(2)) .

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 b^(2)=ac prove that (1)/(x)+(1)/(z)=(2)/(y)

If a^(x)=b,b^(y)=c and c^(z)=a, prove that xyz=1

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

If (loga)/(y+z)=(log b)/(z+x)=(log c)/(x+y) show that (b/c )^(x)(c /a)^(y)(a/b)^z=1

If x+z = 2y " and " b^2 = ac , then prove that a^(y-z)*b^(z-x)*c^(x-y) =1 .

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