If a,x,y,b are in A.P., prove that (2x-y)(2y-x) = ab`

If p, q, r are in A.P. while x, y, z are in G.P., prove that x^(q-r).y^(r-p).z^(p-q) =1 .

If y = sin^-1x , prove that (1-x^2)y_2 - x y_1= 0

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 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^2/a^2 + y^2/b^2 = 1 , prove that (d^2y)/(dx^2) = -(b^4)/(a^2y^3)~

If the points (x,y),(a,0) and (0,b) are collinear, prove that x/a + y/b = 1, ab ne 0

If y = x^x , prove that y_2 - y^-1 (y_1)^2 - yx^-1 = 0

If y = 2 cos x -6 sin x , prove that (d^2y)/(dx^2)+y = 0

If x^2/a^2 - y^2/b^2 = 1 , prove that ((d^2y)/dx^2) = (-b^4)/(a^2y^3)