 Hi, and welcome to the session, I am Deepika here. Let's discuss the question, find the principal value of cos inverse minus 1 by 2. So before finding the principal value of cos inverse minus 1 by 2, let us look at the table. In this table, the domains and ranges of inverse trigonometric functions are given. So we want the range of the principal value branch of cos inverse which is close interval 0 to pi. So this is the key idea behind our question. So let's discuss the solution. Let cos inverse minus 1 by 2 is equal to y then cos y is equal to minus 1 by 2 which is equal to minus cos pi by 3. So this is equal to cos of pi minus pi by 3 and this is equal to cos 2 pi by 3. Now we know that the range of principal value branch close interval 0 to pi 2 pi by 3 minus 1 by 2. Therefore, the principal value of minus 1 by 2 is pi by 3 and this is the answer for the above question. I hope the question is clear to you. I enjoy yourself.