 Hi and how are you all today? I am Priyanka and let us proceed on with the question which is given to us. It says find the principle and general solution of the following equations. Now the first equation given to us is tan x is equal to root 3 where we need to find the principle as well as the general solution for x. Let us proceed on with our solution. As we know that the value of tan x, if we draw a quadrant this is the first quadrant, this is the second, this is the third and this is the fourth quadrant, right? Now here in first quadrant we know that both sin and cos are positive and then here we know that sin is negative but cos, here x and y both are positive, here x is negative, y is positive, here both are negative and here we have x as positive and y as negative, right? Now here the value of tan x is given to us in positive so that means it will lie in the first quadrant and it will lie either in the third quadrant. So we need to find the values for the first quadrant and the second quadrant. So tan x it is given to us as root 3. We know that the value of tan x in the first quadrant comes out to be pi by 3, right? But this is the value which is in the first quadrant, right? Now we need to find a value that is in the third quadrant so that means we need to add pi by 3 to pi in order to reach to this third quadrant. So tan x will be equal to tan pi plus pi by 3 which gives us the value as tan 4 pi by 3. So that means the principle solution, the principle solution is the solution that lies between 0 and 2 pi it is pi by 3 and 4 pi by 3. Right proceed on to find the general solution of the theorems that is the third theorem sees that tan x is equal to tan y it implies that x is equal to n pi plus y where n belongs to the set of integers and also if n x x and y are not odd multiples of pi by 2, right? So here we have tan x equals tan y and here y will be taken as pi by 3. So the general solution comes out to be x is equal to n pi plus pi by 3 where n belongs to set. So this is the answer to the general solution this is the principle solution which we were supposed to find out and this is the general solution which we were supposed to find out in the question. So I hope you enjoyed the session to remember that whenever you are given a value just think that that if that value is positive in which quadrant it will lie if that value is negative in which quadrant it will lie then find out the values in those two quadrants respectively that will form your principle solution and then for your general solution refer to the theorems that has been explained to you in your course. So bye for now.