 Hello and welcome to the session. In this session we discussed the following question which says evaluate cos pi by 2 minus cot inverse minus 1 upon root 3. Let's move on to the solution now. We need to evaluate cos pi by 2 minus cot inverse minus 1 upon root 3. We know that the range of principal value of cot inverse is the open interval 0 pi. So we take let cot inverse minus 1 upon root 3 be equal to say y. So from here we get that cot y is equal to minus 1 upon root 3 or you can say that cot y is equal to minus cot of pi by 3. Since we know that the value for cot pi by 3 is 1 upon root 3 so minus cot pi by 3 would be equal to minus 1 upon root 3. We can also say that cot y is equal to cot 2 pi by 3 that is instead of minus cot pi by 3 we are between cot 2 pi by 3. So this means that y is equal to 2 pi by 3 which belongs to the open interval 0 pi and we have taken y to be equal to cot inverse of minus 1 upon root 3. So we say that cot inverse of minus 1 upon root 3 is equal to 2 pi by 3. Now putting this value of cot inverse minus 1 upon root 3 in the given expression we get cos of pi by 2 minus cot inverse of minus 1 upon root 3 is equal to cos of pi by 2 minus 2 pi by 3 and this would be further equal to cos of minus pi by 6 which is equal to minus of cos pi by 6 and we know that the value of cos pi by 6 is root 3 by 2 so this is equal to minus of root 3 by 2. Hence we get cos pi by 2 minus cot inverse minus 1 upon root 3 is equal to minus root 3 by 2. So this is our final answer this completes the session hope you have understood the solution of this question.