 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, discuss the continuity of the following functions. Function f is given by fx equal to sin x minus cos x. We know any function f is continuous at x equal to a if it is defined at x equal to a or we can say f a exists and limit of the function is equal to value of the function at x equal to a. This is the key idea to solve the given question. Now let us start the solution. We are given function f given by fx equal to sin x minus cos x. We know sin x is defined at every real number. Cos x is also defined at every real number. So their difference is also defined at every real number. So we can say function f is defined at every real number. Let a be any real number now. Function f is defined at real number a. Now let us find out limit of the function at x equal to a. So we can write limit of x tending to a fx is equal to limit of x tending to a sin x minus cos x. Now put x equal to a plus h then as x tends to a h tends to 0. Now we can write this limit of h tending to 0 sin a plus h minus cos a plus h. Now we know sin a plus p is equal to sin a cos p plus cos a sin p. So we will apply formula of sin a plus p here. Now we can write sin a cos h plus cos a sin h. Now we know cos a plus p is equal to cos a cos p minus sin a sin p. So here we can write cos a cos h minus sin a sin h. This is equal to limit of h tending to 0 sin a cos h plus cos a sin h minus cos a cos h sin a sin h. Now this is equal to sin a cos 0 plus cos a sin 0 minus cos a cos 0 plus sin a sin 0. Now this is equal to sin a multiplied by 1 we know cos 0 is equal to 1 cos a multiplied by 0 we know sin 0 is equal to 0 minus cos a multiplied by 1 plus sin a multiplied by 0. Now this is equal to sin a minus cos a. So we get limit of x tending to a f x equal to sin a minus cos a. Now value of the function at x equal to a is given by f a which is equal to sin a minus cos a. Now clearly we can see limit of the function is equal to value of the function at x equal to a. So given function is continuous at real number a. Now we can write limit of the function that is limit of x tending to a f x is equal to f a is equal to sin a minus cos a. This implies function f is continuous at x equal to a. Now since function f is continuous at real number a so we can write function f is continuous at every real number. So this is our required answer. This completes the session. Hope you understood the session. Take care and have a nice day.