 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, what is the maximum value of the function sine x plus cos x? Now let us start the solution. First of all, let us assume function f is given by fx equal to sine x plus cos x. Now differentiating both sides with respect to x, we get f dash x equal to cos x minus sine x. Now to find the critical value of x, we will put f dash x equal to 0. This implies cos x minus sine x is equal to 0. Now this implies cos x is equal to sine x and we can write sine x upon cos x is equal to 1. Now we know sine x upon cos x is equal to tan x. So we can write tan x is equal to 1. Now we know this is possible only when x is equal to pi upon 4 and 5 pi upon 4. Now let us find out f pi upon 4, f pi upon 4 is equal to sine pi upon 4 plus cos pi upon 4. Now this is equal to 1 upon root 2 plus 1 upon root 2 which is further equal to 2 upon root 2. Now on rationalizing, we get 2 root 2 upon 2. 2 and 2 will get cancelled and we get f pi upon 4 equal to root 2. Now let us find out value of the function. It takes equal to 5 pi upon 4. This is equal to sine pi upon 4 plus cos pi upon 4. Now this is equal to minus 1 upon root 2 plus minus 1 upon root 2. Now this can be written as minus 2 upon root 2. Now on rationalizing, we get minus 2 upon root 2 upon 2. 2 and 2 will cancel each other and we get minus root 2. So value of the function takes equal to 5 pi upon 4 is equal to minus root 2. So we get maximum value of the function f is root 2. So this is our required answer. This completes the session. Hope you understood the session. Take care and goodbye.