 Hello and welcome to the session. Let us understand the following question which says, if x and y are connected parametrically by the equation given without eliminating the parameter find dy by dx, x is equal to cos theta minus cos tau theta and y is equal to sin theta minus sin tau theta. Now let us proceed on to the solution. The given equations are x is equal to cos theta minus cos 2 theta and y is equal to sin theta minus sin 2 theta. Now let us find the derivatives of x and y with respect to theta. Therefore, dx by dx theta is equal to minus sin theta plus 2 sin 2 theta and dy by dx theta is equal to cos theta minus 2 cos 2 theta. dx by dx theta can be written as 2 sin 2 theta minus sin theta. Therefore, dy by dx is equal to dy by dx theta divided by dx by dx theta which is equal to dy by dx theta is cos theta minus 2 cos 2 theta divided by 2 sin 2 theta minus sin theta which is equal to dy by dx theta minus 2 cos 2 theta divided by 2 sin 2 theta minus sin theta. If you have understood this question, that is all for the session. Bye and have a nice day.