 Hello and welcome to the session, the given question says prove that 1 divided by cosec theta minus cot theta minus 1 divided by sin theta is equal to 1 divided by sin theta minus 1 divided by cosec theta plus cot theta. So, let us start with the solution and we shall be solving both the left hand side and right hand side and show that after solving we get the same terms. So, let us start the left hand side we have 1 divided by cosec theta minus cot theta minus 1 divided by sin theta this is equal to 1 divided by sin theta minus 1 divided by cosec theta plus cot theta or it can further be written as 1 divided by cosec theta minus cot theta minus 1 divided by sin theta is cosec theta this is equal to again 1 divided by sin theta is cosec theta minus 1 divided by cosec theta plus cot theta. Now, we know that cosec square theta is equal to 1 plus cot square theta therefore, cosec square theta minus cot square theta is equal to 1 and this can further be written as cosec theta minus cot theta into cosec theta plus cot theta is equal to 1 right. So, here in case of 1 let us substitute cosec theta minus cot theta into cosec theta plus cot theta. So, we have cosec theta minus cot theta into cosec theta plus cot theta whole divided by cosec theta minus cot theta minus cosec theta this is equal to cosec theta minus cosec theta minus cot theta into cosec theta plus cot theta divided by cosec theta plus cot theta and now canceling cosec theta minus cot theta by cosec theta minus cot theta and here also cosec theta plus cot theta by cosec theta plus cot theta. We have on the left hand side cosik theta plus cot theta minus cosik theta is equal to cosik theta minus cosik theta minus cot theta. Now canceling cosik theta with minus cosik theta and here also canceling cosik theta with minus cosik theta. On the left hand side we have cot theta and on the right hand side also we have cot theta. So this shows that left hand side is equal to the right hand side. Hence we have 1 divided by cosik theta minus cot theta minus 1 divided by sin theta is equal to 1 divided by sin theta minus 1 divided by cosik theta plus cot theta. So this completes the solution. Hope you have understood it. Bye and take care.