 Hello and welcome to this session let us understand the following problem today write the following function in the simplest form we have tan inverse of 3a square x minus x cube by a cube minus 3x square where a is written as 0 and minus a by root 3 is less than equal to x is less than equal to a by root 3. Now let us write the solution put x is equal to a tan theta then x by a is equal to tan theta therefore theta is equal to tan inverse x by a let us name this as 1. Now first of 3a square x minus x cube by a cube minus 3a x square is equal to tan inverse of 3a square putting x is equal to a tan theta then again a tan theta whole cube whole divided by a cube minus 3a into a tan theta the whole square which is equal to tan inverse of 3a cube tan theta minus a cube tan cube theta by a cube minus 3a cube tan square theta which is equal to tan inverse of taking a cube common we get 3 tan theta minus tan cube theta again from denominated taking a cube common we get 1 minus 3 tan square theta this gets cancels so we are left with tan inverse of tan 3 theta because we have this identity which is tan 3a is equal to 3 tan a minus tan cube a divided by 1 minus 3 tan square a so this gets equal to 3 theta which is equal to 3 into tan inverse x by a from 1 thus the required answer is 3 tan inverse x by a I hope you understood the problem bye and have a nice day