 Hello and welcome to the session. In this session, we discussed the following question that says, solve for x tan inverse 3x plus tan inverse 2x is equal to pi by 4. Before we move on to the solution, let's recall one result according to which we have tan inverse x plus tan inverse y is equal to tan inverse of x plus y, this whole upon 1 minus xy. This is the key idea that we use for this question. Let's proceed with the solution now. We are given tan inverse 3x plus tan inverse 2x is equal to pi by 4. We have to find the value for x. Now on the left hand side, we can apply this formula given in the key idea and using this we get tan inverse of 3x plus 2x upon 1 minus 3x into 2x. This is equal to pi by 4. So further, tan inverse 5x upon 1 minus 6x square is equal to pi by 4. Or you can say we have 5x upon 1 minus 6x square is equal to tan pi by 4 and we know that the value for tan pi by 4 is 1. So we get 5x upon 1 minus 6x square is equal to 1. This gives us 5x is equal to 1 minus 6x square or 6x square plus 5x minus 1 is equal to 0. Now we split the middle term of this quadratic equation. So we get 6x square plus 6x minus x minus 1 is equal to 0. Now taking 6x common here from these two terms we get inside the bracket x plus 1 and we take minus common from these two terms. So minus 1 into x plus 1 this is equal to 0. Or you can say we have x plus 1 into 6x minus 1 is equal to 0. That is x plus 1 equal to 0 or 6x minus 1 equal to 0 which means we have x equal to minus 1 or x equal to 1 upon 6. So these are the two possible values for x. Let's see if x equal to minus 1 and x equal to 1 upon 6 satisfy this equation say equation 1. Now x equal to minus 1 does not satisfy the given equation 1 as the LHS becomes negative when we put x equal to minus 1. Therefore x is not equal to minus 1 and we have x equal to 1 upon 6. Thus x equal to 1 upon 6 is the only solution of the given equation. So this is our final answer. This completes the session. Hope you have understood the solution of this question.