 Hello and welcome to this session. Let us understand the following problem today. If tan inverse of x minus 1 by x minus 2 plus tan inverse of x plus 1 by x plus 2 is equal to pi by 4, then find the value of x. Now let us write the solution. We have tan inverse of x minus 1 by x minus 2 plus tan inverse of x plus 1 by x plus 2, which is equal to pi by 4, which implies tan inverse of x minus 1 by x minus 2 plus tan inverse of x plus 1 by x plus 2, which is equal to tan inverse of 1. This implies tan inverse of x minus 1 by x minus 2 is equal to tan inverse of 1 minus tan inverse of x plus 1 by x plus 2, which is equal to tan inverse of 1 minus x plus 1 by x plus 2 whole divided by 1 plus 1 into x plus 1 by x plus 2, using identity tan inverse x minus tan inverse y, which is equal to tan inverse of x minus y by 1 plus x y. Now this becomes, it's equal to tan inverse of x plus 2 minus x minus 1 by x plus 2 plus x plus 1. This gets cancelled, so we are left with tan inverse of 1 by 2 x plus 3, that is tan inverse of x minus 1 by x minus 2 is equal to tan inverse of 1 by 2 x plus 3, which implies x minus 1 by x minus 2 is equal to 1 by 2 x plus 3. Now solving this we get which implies x minus 1 into 2x plus 3 is equal to x minus 2, which implies 2x square plus 3x minus 2x plus into minus 3 is equal to x minus 2, which implies 2x square plus x minus 3 is equal to x minus 2. Now solving it further we get 2x square plus x minus x minus 3 plus 2 is equal to 0. This gets cancelled so we are left with 2x square minus 1 is equal to 0, which implies 2x square is equal to 1, which implies x square is equal to 1 by 2, which implies x is equal to plus minus 1 by root 2. Therefore required answer is x is equal to plus minus 1 by root 2. I hope you understood the problem. Bye and have a nice day.