 Hello and welcome to the session. Let us understand the following problem today. Solve the following equation tan inverse 1-x by 1 plus x is equal to 1 by 2 tan inverse of x where x is greater than 0. Now let us write the key idea. 2 tan inverse x is equal to tan inverse 2x by 1 minus x square. This is our key idea we will be using in our problem. Now let us write the solution. We have tan inverse 1 minus x by 1 plus x is equal to tan inverse x which implies 2 tan inverse 1 minus x by 1 plus x is equal to tan inverse x. Let us name it as 1. Now we use the identity in the key idea. So we have our LHS equal to 2 tan inverse 1 minus x by 1 plus x which is equal to tan inverse 2 into 1 minus x by 1 plus x whole divided by 1 minus 1 minus x by 1 plus x the whole square which is equal to tan inverse 2 into 1 minus x by 1 plus x into 1 plus x the whole square divided by 1 plus x the whole square minus 1 minus x the whole square which is equal to tan inverse 2 into 1 minus x into 1 plus x by 4x this gets cancels by 2 so we get tan inverse 1 minus x square by 2x thus we have tan inverse 1 minus x square by 2x which is equal to tan inverse x this is from 1 which implies 1 minus x square by 2x is equal to which is equal to 1 minus x square is equal to 2x square which is equal to 3x square is equal to 1 which is equal to x is equal to plus minus 1 by under root 3 so we have x is equal to plus 1 by root 3 since x is not equal to minus 1 by under root 3 therefore the crime answer is x is equal to 1 by under root 3 I hope you understood the problem bye and have a nice day.