 Hi and how are you all today? I am Priyanka and let us start with the question which is given to us. It says find the principle and general solutions of the following equations. Now here the value of sec x is given to us as 2 and we need to find the principle and the general solutions. Before proceeding on with it we must know that the principle solution will lie between 0 and 2 pi whereas the general solution for cos x is equal to cos y implies x is equal to 2n pi plus minus y where n belongs to the set of integers. This is the general solution and according to term 2 this is how we proceed on when we have the value of cos x. Now this is the key idea that we will use in order to proceed on with our solution. As in the question which we are given we are given the sec x so first of all we will convert it into cos x. So let us start with our solution. The value of sec x is given to us as 2. So that means 1 upon cos x is equal to 2 and the reciprocal on doing the reciprocal we have cos x as 1 by 2. Now what is the value of x when cos x is 1 by 2 that comes out to be cos pi by 3 is equal to 1 by 2. Also cos 2 pi as we know that cos x repeats after an interval of 2 pi 2 pi minus pi by 3 will be equal to cos 5 pi by 3 will also give us the value 1 by 2. So that means principal solution is pi by 3 and 5 pi by 3. Right, proceeding on to find the general solution as discussed above cos x is equal to cos y that implies that x is equal to 2n pi plus minus y. Now here our cos x is equal to cos pi by 3. Right, so that means x will be equal to 2n pi plus minus pi by 3 as y is equal to pi by 3. Right, we have just substituted the value of y above mentioned theorem that will help us in finding the general solution. And do remember that here n belongs to the set of integers. So the principal solution comes out to be pi by 3 and 5 pi by 3 whereas the general solution comes out to be x is equal to 2n pi plus minus pi by 3 where n belongs to z. So this ends the question that was given to us. I hope you enjoyed this session and now you know how to find the principal solution as well as the general solution. Bye for now.