 Hello and how are you all there? My name is Priyanka and I shall be helping you with the following question. Here says integrate the following. Now the function which is given to us is 1 minus cos x divided by 1 plus cos x. Now proceeding on with the solution we need to integrate this function with respect to dx. Now here we should know that one minus cos theta is equal to 2 sin square theta by 2 and 1 plus cos theta is equal to 2 cos square theta by 2, right? So here the knowledge of these identities will be the key factor to this question. Now here we can write 1 minus cos x as 2 sin square x by 2 divided by 1 plus cos theta that is 1 plus cos x can be written as 2 cos 2 cos square x by 2 into dx. Further on simplifying it we have it equal to integral of tan square x by 2 into dx because sin square x by 2 divided by cos square x by 2 can be written as tan square x by 2, right? So we have further equal to, now the integral of tan square theta is equal to sin square theta minus 1. So we have over here it as sin square theta is x by 2 minus 1 into dx. Further this can be written as integral of sin square x by 2 into dx minus integral of 1 into dx that is further equal to tan x by 2 divided by 1 by 2 minus x plus c. So the required answer to the question becomes 2 tan x by 2 minus x plus c. Wait, so this is the required answer to the question. Hope you understood it well. Have a nice day ahead.