 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says evaluate cosec 31 degrees minus sec 59 degrees. First of all let us understand that if theta is any acute angle in a right triangle then cosec 90 minus theta is equal to sec theta. This is the key idea to solve the given question. Let us now start the solution. We have to find cosec 31 degrees minus sec 59 degrees. Now we know 31 degrees and 59 degrees are complementary angles. So we can write cosec 31 degrees as cosec 90 degrees minus 59 degrees. We know 90 degrees minus 59 degrees is equal to 31 degrees minus sec 59 degrees. Now from key idea we know cosec 90 minus theta is equal to sec theta. Here cosec 90 minus 59 degrees is equal to sec 59 degrees. Rarely we can see value of theta is 59 degrees here. So we can write this is equal to sec 59 degrees minus sec 59 degrees. Now sec 59 degrees minus sec 59 degrees is equal to 0. So we get cosec 31 degrees minus sec 59 degrees is equal to 0. So 0 is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.