If `b=a+a^2+a^3+ dotoo` prove that `a=b/(1+bdot)`

If b=a+a^(2)+a^(3)+dot oo prove that a=(b)/(1+b)

In a parallelogram A B C D , the bisector of /_A also bisects B C at Xdot prove that A D=2A Bdot

In Figure, X and Y are two points on equal sides A B and A C of a A B C such that A X=A Ydot Prove that X C=Y Bdot

If the derivative of tan^(-1)(a+b x) take the value of 1 at x=0, prove that 1+a^2=bdot

If the points (a ,\ 0),\ (0,\ b)a n d\ (1,\ 1) are collinear, prove that a+b=a bdot

If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove that 1+a^2=bdot

If y=sinx^(sinx^(sinx^dotoo)) , prove that (dy)/(dx)=(y^2cotx)/((1-ylogsinx))

If y=cosx^(cosx^(cosx^dotoo)) , prove that (dy)/(dx)=-(y^2tanx)/((1-ylogcosx))

Two circle with centres A and B intersect at C and Ddot Prove that /_A C B=/_A D Bdot

In Fig. if E F|| D C|| A Bdot Prove that (A E)/(E D)=(B F)/(F C) . (FIGURE)