 Hello and welcome to this session. Let us understand the following problem today. Find the value of the expression. Given to us is tan of sin inverse 3 by 5 plus cot inverse 3 by 2. Now let us write the solution. First of all let us try to bring this sin inverse 3 by 5 and cot inverse 3 by 2 in the form of tan. So we have let 3 by 5 is equal to theta which implies sin theta is equal to 3 by 5. Now tan theta is equal to sin theta by cos theta which is equal to sin theta by 1 minus sin square theta which is equal to 3 by 5 whole divided by 1 minus 3 by 5 the whole square which is equal to 3 by 5 whole divided by 1 minus 9 by 25 which is equal to 3 by 5 divided by under root 16 by 25 which is equal to 3 by 5 divided by 4 by 5 which is equal to 3 by 4 therefore theta is equal to tan inverse 3 by 4 thus sin inverse 3 by 5 is equal to tan inverse 3 by 4 let us name it as 1. Now we have to find the value of cot inverse 3 by 2 we have the identity tan inverse of 1 by x is equal to cot inverse of x where x is greater than 0 so therefore cot inverse of 3 by 2 is equal to tan inverse of 3 by 2 let us name it as 2 Now substituting 1 and 2 in the given expression we get sin inverse 3 by 5 plus cot inverse 3 by 2 is equal to tan of tan inverse 3 by 4 plus tan inverse which is equal to tan of tan in 4 plus 2 by 3 whole divided by 1 minus 3 by 4 into 2 by 3 using the identity tan inverse x plus tan inverse y which is equal to tan inverse of x plus y by 1 minus xy now this becomes is equal to tan of tan inverse 9 plus 8 by 12 whole divided by 12 minus 6 by 12 which is equal to tan of tan inverse of 17 by 6 which is equal to 17 by 6 therefore the required answer is 17 by 6 I hope you understood the problem bye and have a nice day