If reciprocals of `(y-x),2(y-a), (y-z)` are in A.P., prove that `x-a,y-a,z-a` are in G.P.

If y-z,2(y-a),y-x are in H.P. prove that x-a,y-a,z-a are in G.P.

If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that xy,zx,yz are in A.P.

If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany ,tanz are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If sin(y+z-x),sin(z+x-y),"sin"(x+y-z) are in A.P., then t a n x ,tany ,tanz are in (a)A.P. (b) G.P. (c) H.P. (d) none of these

If distinct numbers x,y,z are in G.P. and 1/(x+a),1/(y+a),1/(z+a) are in A.P., prove that a=y .

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

If (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then prove that x ,y ,z are in H.P.

If (a-x)/(p x)=(a-y)/(q y)=(a-z)/ra n dp ,q ,a n dr are in A.P., then prove that x ,y ,z are in H.P.

If x,1,z are in A.P. x,2,z are in G.P., show that 1/x,1/4,1/z are in A.P.

a, b, x are in A.P., a,b,y are in G.P. and a, b, z are in H.P. then: