 Hello and welcome to the session. Let's work out the following problem. It says without using trigonometric tables evaluate the following. So let's now move on to the solution. The given expression is cos 58 degrees upon sin 32 degrees plus sin 22 degrees upon cos 68 degrees minus cos 38 degrees into cosecant 52 degrees upon tan 18 degrees into tan 35 degrees into tan 60 degrees into tan 72 degrees into tan 55 degrees. Now we'll see that in this term some of the angles is 90 degrees. So we'll convert either cos 58 into sin 32 or sin 32 into cos 52. So we'll convert cos as sin 32. So cos 58 degrees can be written as cos 90 minus 32 degrees upon sin 32 degrees plus here again we'll convert cos into sin. Sin 22 degrees upon cos 68 degrees can be written as cos 90 minus 22 degrees plus it's minus cos 38 degrees into cosecant 52 degrees can be written as cosecant 90 minus 38 degrees upon tan 18 degrees to tan 35 degrees into tan 60 degrees which is root 3 into tan 72 degrees can be written as tan 90 minus 18 degrees into tan 55 degrees can be written as tan 90 minus 35 degrees. Now cos 90 minus theta is sin theta so this becomes sin 32 degrees upon sin 32 degrees plus sin 22 degrees upon again cos 90 minus theta is sin theta so it becomes sin 22 degrees minus cos 38 degrees into cosecant 90 minus theta is secant theta so it becomes secant 38 degrees upon tan 18 degrees into tan 35 degrees into root 3 into tan 90 minus theta is cot theta so tan 90 minus 18 degrees is cot 18 degrees into tan 90 minus 35 degrees is cot 35 degrees and here you must write the formulae which you have used cos 90 minus theta is equal to sin theta and cosecant 90 minus theta is equal to cos theta is secant theta and tan 90 minus theta is cot theta and it is very important to write all the formulae which you are using now sin 32 degrees gets cancelled with sin 32 degrees sin 22 degrees gets cancelled with sin 22 degrees and here we have 1 plus 1 minus cos 38 degrees into secant 38 degrees can be written as 1 upon cos 38 degrees upon tan 18 degrees into tan 35 degrees into root 3 into cot 18 degrees can be written as 1 upon tan 18 degrees into cot 35 degrees can be written as 1 upon tan 35 degrees right here because cos theta is equal to 1 upon secant theta and cot theta is equal to 1 upon tan theta right now tan 18 degrees gets cancelled with tan 18 degrees tan 35 degrees gets cancelled with tan tan 35 degrees cos 38 degrees cos 38 degrees so we have 1 plus 1 that is 2 minus here in the numerator we have 1 upon 1 into root 3 so this is 2 minus 1 upon root 3 now again 2 minus 1 upon root 3 rationalizing 1 upon root 3 multiplied by root 3 by root 3 that is 1 so we have 2 minus 1 into root 3 is root 3 upon root 3 into root 3 is 3 now taking LCM LCM would be 3 3 into 2 is 6 minus root 3 so the value of the given expression is 6 minus under the root 3 upon 3 so this completes the question and the session why for now take care have a very nice day