 Hello and welcome to the session. In this session we discussed the following question which says, what is the value of sin inverse minus root 3 by 2 plus 3 tan inverse root 3? Let's move on to the solution now. We need to find the value for sin inverse minus root 3 by 2 plus 3 tan inverse root 3. Now we know that the range of principal value of sin inverse is the closed interval minus pi by 2 pi by 2. So we take let sin inverse minus root 3 by 2 be equal to y. So this means we get sin y is equal to minus root 3 by 2 or you can say we have sin y is equal to sin of minus pi by 3. So this means we get y is equal to minus pi by 3 which belongs to the closed interval minus pi by 2 pi by 2. Now we had taken y to be equal to sin inverse of minus root 3 by 2. Therefore we get y is equal to sin inverse of minus root 3 by 2 is equal to minus pi by 3. Next we know that the range of principal value of tan inverse is open interval minus pi by 2 pi by 2. So let's take tan inverse root 3 be equal to some theta. So this means that tan theta is equal to root 3 or you can say that tan theta is equal to tan pi by 3 since the value of tan pi by 3 is root 3. From where we get theta is equal to pi by 3 which belongs to the open interval minus pi by 2 and we have taken theta to be equal to tan inverse root 3 therefore we get theta is equal to tan inverse root 3 is equal to pi by 3. Thus the given expression which is sin inverse minus root 3 by 2 plus 3 into tan inverse root 3 would be equal to the value for sin inverse minus root 3 by 2 is minus pi by 3. So this is equal to minus pi by 3 plus 3 into the value for tan inverse root 3 which is equal to pi by 3. This 3 cancels with this 3 and so this is equal to minus pi by 3 plus pi which is equal to 2 pi by 3. So finally we get sin inverse of minus root 3 by 2 plus 3 into tan inverse of root 3 is equal to 2 pi by 3. So this is our final answer. This completes the session. Hope you have understood the solution of this question.