 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says show that tan 48 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees multiplied by tan 67 degrees is equal to 1. First of all let us understand that if in any right triangle theta is any of the acute angles then tan 90 minus theta is equal to cot theta also cot theta is equal to residue local of tan theta or we can say cot theta is equal to 1 upon tan theta. This is the K idea to solve the given question let us now start the solution. We have to show that tan 48 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees multiplied by tan 67 degrees is equal to 1. Now first of all let us take left hand side that is tan 48 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees multiplied by tan 67 degrees. Now we know complementary angle of 48 degrees is 42 degrees so we can write tan 48 degrees as tan 90 minus 42 degrees. So this is equal to tan 90 minus 42 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees. Here we know complementary angle of 67 degrees is 23 degrees so we can write tan 67 degrees as tan 90 minus 23 degrees. Now we know tan 90 degrees minus theta is equal to cot theta. Here value of theta is 42 degrees so we can write it equal to cot 42 degrees so this is equal to cot 42 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees. Here also we know tan 90 minus theta is equal to cot theta. Here value of theta is 23 degrees so we can write it as cot 23 degrees. Now we know cot theta is equal to 1 upon tan theta so we can write cot 42 degrees is equal to 1 upon tan 42 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees multiplied by cot 23 degrees is equal to 1 upon tan 23 degrees. We know cot theta is equal to 1 upon tan theta so here cot 23 degrees can be written as 1 upon tan 23 degrees. Now tan 42 degrees will get cancelled by tan 42 degrees and here tan 23 degrees will cancel tan 23 degrees so we get final answer is equal to 1. Now clearly we can see left hand side is equal to 1 is equal to right hand side so we get tan 48 degrees multiplied by tan 23 degrees multiplied by tan 42 degrees multiplied by tan 67 degrees is equal to 1. This completes the session. Hope you understood the solution. Take care and have a nice day.