 Hello and welcome to the session. Let us understand the following problem today. Write the following function in the simplest form. We have tan inverse of x square root a square minus x square where mod of x is less than a. Now, let us write the solution. Put x is equal to a sin theta. Let us name this equation as 1. Therefore, we have tan inverse of x square root a square minus x square is equal to tan inverse of a sin theta by under root a square minus a square sin square theta which is equal to tan inverse of a sin theta by under root a square taking common we get 1 minus sin square theta which is equal to tan inverse of a sin theta by under root a square cos square theta which is equal to tan inverse of a sin theta by a cos theta. Here a get cancelled so we are left with tan inverse of tan theta which is equal to theta. Now, x is equal to a sin theta. Therefore, x by a is equal to sin theta which implies theta is equal to sin inverse x by a. Therefore, putting this value of theta here we get our required answer as sin inverse x by a. I hope you understood the problem. Bye and have a nice day.