 Hello and welcome to this session. Let us understand the following problem today. Find the value of the following tan half sin inverse 2x by 1 plus x square plus cos inverse 1 minus y square by 1 plus y square where mod of x is less than 1, y is greater than 0 and x is less than 1. Let us write this solution. We have to find the value of tan half sin inverse of 2x by 1 plus x square plus cos inverse of 1 minus y square plus 1 by plus y square which can be written as tan half tan inverse x plus 2 tan inverse y because x by 1 plus x square is equal to 2 tan inverse x for all x belongs to minus 1, 1 and cos inverse of 1 minus y square by 1 plus y square is equal to 2 tan inverse y for all y greater than 0. Now this becomes now which is equal to tan of half taking 2 common value with tan inverse x plus tan inverse y which is equal to tan of this get cancels so tan inverse x plus tan inverse y which is equal to tan of tan inverse x plus y by 1 minus xy which is equal to x plus y by 1 minus xy therefore the required answer is x plus y by 1 minus xy. I hope you understood the problem. Bye and have a nice day.