 Hello and welcome to the session. Let's work on the following problem. It says evaluate without trigonometric tables. So let's now move on to the solution. We have to evaluate this expression without using trigonometric table. The given expression is secant square 90 minus theta minus cot square theta upon 2 into sine square 25 degrees plus sine square 65 degrees plus 2 into cot square 60 degrees into tan square 28 degrees into tan square 62 degrees upon 3 into secant square 43 degrees minus cot square 47 degrees. Now we know that secant 90 minus theta is cosecant theta. So it becomes cosecant square theta minus cot square theta upon sine square 25 degrees. Now sine square 65 degrees can be written as sine square 90 minus 25 degrees. In these type of questions you try to use the trigonometric identity which you know very well. So this becomes 2 into cot square 60 degrees into tan square 28 degrees and tan square 62 degrees can be written as tan square 90 minus 28 degrees upon 3 into secant square 43 degrees minus. Now you know that secant square theta minus tan square theta is 1. So you convert cot theta into tan theta and you know how to do that. It can be written cot 47 degrees can be written as 90 minus 43 degrees and here you must write the identity which we have used that secant 90 minus theta is equal to cosecant theta. Now again this is equal to cosecant square theta minus cot square theta is 1 upon 2 into sine square 25 degrees plus cos square 25 degrees because sine 90 minus theta is cos theta plus 2 into cos square 60 degrees into tan square 28 degrees. Now we know that tan 90 minus theta is cot theta. So this becomes cot square 28 degrees upon 3 into secant square 43 degrees minus tan square 43 degrees because cot 90 minus theta is tan theta and here again you write whatever you have used that's sine 90 minus theta is cos theta and 90 minus theta is cot theta and cot 90 minus theta is tan theta and also you have used that cosecant square theta minus cot square theta is 1. You must write all these identities. Now again this is equal to 1 upon 2 into sine square 25 plus cos square 25 degrees is 1 plus 2 into cos square 60 degrees and tan square 28 degrees into cot square 28 degrees is 1 upon 3 into secant square 43 degrees minus tan square 43 degrees is 1. So you have to write that sine square theta plus cos square theta is 1 secant square theta minus tan square theta is 1 and tan theta is equal to 1 upon cot theta or we can say that tan theta into cot theta is 1. So this is equal to 1 upon 2 plus 2 into cos square 60 degrees and cos 60 is 1 by 2. So this becomes 1 by 2 square upon 3 again this is equal to 1 by 2 plus 1 by 2 upon 3. 1 by 2 square is 1 by 4 and 2 gets cancelled with 1 of the 2. 1 by 2 plus 1 by 2 by 3 is 1 by 6 and 1 by 2 plus 1 by 6 is taking calcium in the numerator will have 3 plus 1 upon 6. So this is equal to 4 by 6 which is equal to 2 by 3. Hence the value of the given expression is 2 by 3 and this completes the question and the session. Bye for now. Take care. Do remember all the trigonometric identities. So take care, bye.