 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 multiplied by cos x. First of all let us understand that function f is continuous at x equal to a, function is defined at x equal to a or we can say f a exist 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 with the solution, we are given function f given by fx equal to sin x multiplied by cos x, now we know sin function is defined at every real number, cosine function is also defined at every real number, so their product is also defined at every real number so we can say 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 equal to a, limit of x tending to a fx is equal to limit of x tending to a, sin x multiplied by cos x, now put x equal to a plus h as x tends to a, h tends to 0, now substituting these values in this limit we get limit of h tending to 0, a plus h multiplied by cos a plus h, this can be written as limit of h tending to 0, 1 upon 2 multiplied by 2 sin a plus h multiplied by cos a plus h, here we have done multiplication and division by 2, now this can be written as limit of h tending to 0, 1 upon 2 multiplied by sin 2 a plus h, we know 2 sin theta multiplied by cos theta is equal to sin 2 theta, now this is equal to 1 upon 2 multiplied by sin 2 a plus 0, this is equal to 1 upon 2 multiplied by sin 2 a or you can simply write it as 1 upon 2 2 sin a multiplied by cos a, we know sin 2 a is equal to 2 sin a cos a, this is equal to sin a multiplied by cos a, so we get limit of x tending to a f x equal to sin a multiplied by cos a, let us now find out value of the function at x equal to a, f a is equal to sin a multiplied by cos a, now clearly we can see limit of the function is equal to value of the function at x equal to a, so this implies even function f is continuous at real number a, now we get function f is continuous at every real number a, so we can write even function f is continuous at every real number a, this is our required answer, this completes the session, hope you understand the session, take care and keep smiling.