 Hello and welcome to the session. In this session we discuss the following question that says show that tan inverse of x squared plus x to the power 3 by 2 upon 1 minus x to the power 7 by 2 is equal to tan inverse x squared plus tan inverse x to the power 3 by 2. This is what we have to show. Before we move on to the solution let's recall one formula which says tan inverse x plus tan inverse y is equal to tan inverse of x plus y upon 1 minus xy. This is the key idea that we use for this question. Now let's see the solution. We need to show that tan inverse x squared plus x to the power 3 by 2 upon 1 minus x to the power 7 by 2 is equal to tan inverse x squared plus tan inverse x to the power 3 by 2. This is what we have to show. Let's consider the RHS which is tan inverse x squared plus tan inverse x to the power 3 by 2. Here we can apply the formula tan inverse x plus tan inverse y is equal to tan inverse x plus y upon 1 minus xy. So in place of x we would take x squared and in place of y here we would take x to the power 3 by 2 and so this would be equal to tan inverse x squared plus x to the power 3 by 2 upon 1 minus x squared into x to the power 3 by 2. So this is further equal to tan inverse x squared plus x to the power 3 by 2 upon 1 minus x to the power 7 by 2 which is same as the LHS. Thus we get the RHS is equal to the LHS and this is what we were supposed to prove. So hence proved this completes the session. Hope you have understood the solution of this question.