 Hi and welcome to the session. Let us discuss the following question. Question says, if sec 4a is equal to cosec A minus 20 degrees where 4a is an acute angle, find the value of A. 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. Now let us start the solution. We are given sec 4a is equal to cosec A minus 20 degrees. Now we know sec theta is equal to cosec 90 minus theta. Here we can write sec 4a is equal to cosec 90 minus 4a. Here value of theta is equal to 4a. So we can write it equal to cosec 90 minus 4a. Now cosec 90 degrees minus 4a is equal to cosec A minus 20 degrees. Now we know cosec 90 degrees minus 4a is equal to cosec A minus 20 degrees only when value of these two angles is equal to each other. So we can write this implies 90 degrees minus 4a is equal to A minus 20 degrees. Now adding 20 on both the sides we get 110 degrees minus 4a is equal to A. Adding 4a on both the sides we get 110 degrees is equal to 5a. Now dividing both the sides by 5 we get 110 degrees upon 5 is equal to A. Now we will cancel common factor 5 from numerator and denominator both and we get 22 degrees is equal to A or we can simply write it as A is equal to 22 degrees. So our required answer is angularly is equal to 22 degrees. This completes my session. Hope you understood the solution. Take care and have a nice day.