 Hi and welcome to the session. Let's work out the following question. The question says evaluate limit x approaching to 0 square root 1 plus x minus square root 1 minus x divided by sine x. So let's start with the solution to this question. Now this can be written as limit x approaching to 0 square root 1 plus x minus square root 1 minus x multiplied by square root 1 plus x plus square root 1 minus x divided by sine x into square root 1 plus x plus square root 1 minus x. Now what we have done here is we have rationalized the limit. Now this is equal to limit x approaching to 0. Now this can be written as 1 plus x minus 1 minus x divided by sine x into square root 1 plus x plus square root 1 minus x. Now here we have applied the formula a minus b into a plus b is equal to a square minus b square wherein a is square root 1 plus x and b is square root 1 minus x. Now this can be further written as limit x approaching to 0 into 2x divided by sine x multiplied by 1 upon square root 1 plus x plus square root 1 minus x. Now we know that limit x approaching to 0 x divided by sine x is equal to 1. So we have 2 into 1 into 1 divided by square root of 1 plus 0 plus square root 1 minus 0 and this we get by putting x to be equal to 0. So this is equal to 2 into 1 into 1 upon 2 and that is equal to 1. So our answer to this question is 1. I hope that you understood this illusion and enjoyed the session. Have a good day.