 Hi and welcome to the session. Let us discuss the following question. Question says if tan A is equal to cot B, prove that A plus B is equal to 90 degrees. First of all let us understand that if theta is any acute angle of right triangle then tan 90 minus theta is equal to cot theta. This is the key idea to solve the given question. Let us now start the solution. We have given that tan A is equal to cot B. Now we know cot theta is equal to tan 90 minus theta. Here value of theta is B so cot B can be written as tan 90 degrees minus B. So we get tan A is equal to tan 90 degrees minus B. Now we know tan A is equal to tan 90 degrees minus B only when these two angles are equal. So we can write this implies A is equal to 90 degrees minus B. Now adding B on both the sides we get A plus B is equal to 90 degrees. So therefore A plus B is equal to 90 degrees hence proved. This completes the session. Hope you understood the solution. Take care and have a nice day.