 Hi, and how are you all today? The question says, find the equation of the tangent and the nominal to the curve x is equal to 1 minus cos theta y is equal to theta minus sin theta at theta is equal to pi by 4. So here we are given two equations that is x is equal to 1 minus cos theta and y is equal to theta minus sin theta. We need to differentiate these both equations with respect to theta. So this implies dx by d theta is equal to minus of minus minus sin theta. So this implies dx by d theta is equal to sin theta as minus minus will become plus over here. Similarly here we will find out dy by d theta it will be 1 minus cos theta right. So this means dy by dx will be equal to what? It will be 1 minus cos theta upon dx by d theta that is sin theta. Now we will find out dy by dx and theta is equal to pi by 4. So it is 1 minus cos pi by 4 divided by sin pi by 4 that is equal to 1 minus 1 by root 2 upon 1 upon root 2. This further gives us root 2 minus 1 upon root 2 getting divided by 1 by root 2 which is further equal to root 2 minus 1. So we have slope of tangent equal to dy by dx and that we have found out to be root 2 minus 1 whereas slope of normal is minus dx by dy. So it is minus 1 upon root 2 minus 1. Now we need to find out the value of x1 and y1 also. So when theta is equal to pi by 4 we have the value of x as root 2 minus 1 upon root 2 and we have the value of y as pi by 4 plus 1 by root 2 that is by just substituting the value of theta as pi by 4 in these two equations we have their values. Now we can easily find out equation of the tangent that is y minus y1. So it is y minus pi by 4 plus as minus minus will become plus plus 1 by root 2 is equal to dy by dx that is found out above as root 2 minus 1 into x minus x1 that is root 2 minus 1 upon root 2 whereas equation of normal is y minus y1 equal to minus 1 upon dy by dx that is root 2 minus 1 into x minus x1. Right? So these two are the required answer to the given question. Right? So hope you understood the whole concept well and enjoyed it too. Have a nice day ahead.