 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 fx is equal to sin x plus cos x. First of all let us understand that function f is continuous at x is equal to a if function is defined at x is equal to a or we can say f a exist. Limit of the function is equal to value of the function at x is equal to a. This is the key idea to solve the given question. Let us now start with the solution. We know function f is given by fx is equal to sin x plus cos x. We know sin function is defined at every real number and cosine function is also defined at every real number. So their sum is also defined at every real number. So we can write function f is defined at every real number. Now let a be any real number. Let us now find out limit of the function at x is 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 plus cos x. Now let us put x is equal to a plus h then as x tends to a h tends to 0. Now we can write this limit as limit of h tending to 0 sin a plus h plus cos a plus h. Now here we will apply the formula for sin a plus b. We know sin a plus b is equal to sin a cos b plus cos a sin b. So we can write it equal to limit of h tending to 0 sin a cos h plus cos a sin h and we know here we will apply the formula for cos a plus b and cos a plus b is equal to cos a cos b minus sin a sin b. So we can write it as cos a cos h minus sin a sin h. Now this is further equal to sin a multiplied by limit of h tending to 0 cos h plus cos a multiplied by limit of h tending to 0 sin h plus cos a multiplied by limit of h tending to 0 cos h minus sin a multiplied by limit of h tending to 0 sin h. Now this is further equal to sin a cos 0 plus cos a sin 0 plus cos a cos 0 minus sin a sin 0. Now we know cos 0 is equal to 1 and sin 0 is equal to 0. Now substituting the corresponding values of cos 0 and sin 0 in this expression we get sin a multiplied by 1 plus cos a multiplied by 0 plus cos a multiplied by 1 minus sin a multiplied by 0. Now simplifying we get sin a plus cos a. These two terms will become 0 as we know anything multiplied by 0 is equal to 0. So we get limit of x tending to a fx is equal to sin a plus cos a. Let us now find out value of the function at x is equal to a f a is equal to sin a plus cos a. Clearly we can see limit of the function is equal to value of the function at x is equal to a. So we can write limit of x tending to a fx is equal to f a is equal to sin a plus cos a. Now this implies given function f is continuous at x is equal to a we know a is any real number. So we can write function f is continuous at every real number. Function f is continuous at x is equal to a and we know a can have any real value. So 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 keep smiling.