 Hello and welcome to this session. Let us understand the following problem today. tan inverse xy y minus tan inverse x minus y by x plus y is equal to a pi by 2 b pi by 3 c pi by 4 d minus 3 pi by 4. Now let us first write the formula that we will be using in the problem. tan inverse x plus tan inverse y is equal to tan inverse x minus y by 1 plus xy. Now let us write the solution. We have tan inverse xy y minus tan inverse x minus y by x plus y which is equal to tan inverse of x by y minus x minus y by x plus y whole divided by 1 plus x by y into x minus y by x plus y which is equal to tan inverse of x into x plus y minus x minus y into y by y into x plus y whole divided by x plus y into y plus x into x minus y whole divided by y into x plus y. This gets cancelled. So we have left with tan inverse x square plus xy minus xy plus y square divided by xy plus y square plus x square minus xy. This xy gets cancelled and this xy gets cancelled. So we are left with tan inverse of x square plus y square by x square plus y square. Therefore it is equal to tan inverse of 1 because this gets cancelled with this. So which is equal to pi by 4. Hence the required and the correct answer is C. I hope you understood the problem by and have a nice day.