 Hello and welcome to this session. Let us understand the following problem today. Sign tan inverse x where mod of x is less than 1 is equal to a x by under root 1 minus x square b 1 by under root 1 minus x square c 1 by under root 1 plus x square d x by under root 1 plus x square. Now that is why this variation. Let tan inverse x is equal to alpha then x is equal to tan alpha then sin alpha is equal to x by under root 1 plus x square which implies alpha is equal to sin inverse x by under root 1 plus x square. Now sin of tan inverse x is equal to sin alpha which is equal to sin of sin inverse x by under root 1 plus x square which is equal to x by under root 1 plus x square. Therefore the required answer is d. I hope you understood the problem. Bye and have a nice day.