 Hello and welcome to the session. The given question says evaluate without using the trigonometric tables and we have cos square 90 degrees minus theta minus tan square theta divided by 4 times of cos square 48 degrees plus cos square 42 degrees minus 2 times of tan square 30 degrees into second square 52 degrees into sin square 38 degrees divided by cos square 70 degrees minus tan square 20 degrees. Let's start with the solution and we have to evaluate the value of the following and for evaluating it we shall be using the following values right. These are the six given identities and we shall be using them to evaluate let's proceed on. Now this can be written as cos 90 degrees minus theta whole square and cos 90 degree minus theta is sec theta. So we have sec square theta minus tan square theta whole divided by 4 times of now here we have cos square 48 degrees and this can be written as cos 48 degrees whole square and cos 48 degrees can be written as cos of 90 degrees minus 42 degrees square plus cos square 42 degrees then we have minus 2 times of tan 30 degrees 1 by root 3 and 1 by root 3 whole square gets 1 by 3 into sec square 52 degrees can be written as sec square 90 degrees minus 38 degrees into sin square 38 degrees whole divided by now this can be written as cos square 90 degrees minus 20 degrees minus tan square 20 degrees further it can be written as now we know that sec square theta is equal to 1 plus tan square theta so sec square theta minus tan square theta gives 1 divided by 4 times of this results to cos 90 degrees minus 42 degrees whole square and cos 90 degrees minus theta is sin theta so here we have sin 42 degrees whole square that is sin square 42 degrees plus cos square 42 degrees minus 2 divided by 3 into this is sec 90 degrees minus 38 degrees whole square and sec 90 minus theta is cos theta so this can be written as cos square 38 degrees into sin square 38 degrees divided by cos 90 degrees minus 20 degrees sec 20 degrees and we have whole square minus tan square 20 degrees this is further equal to 1 divided by 4 into 1 since sin square theta plus cos square theta is equal to 1 and we have minus 2 divided by 3 into 1 and this is because cos square 38 degrees is equal to 1 divided by sin square 38 degrees and on cancelling it with sin square 38 degrees we get 1 divided by again we have sec square theta is equal to 1 plus tan square theta therefore sec square theta minus tan square theta is equal to 1 for all the values of theta therefore here sec square 20 degrees minus tan square 20 degrees is again equal to 1 now this is further equal to 1 divided by 4 minus 2 divided by 3 and now taking a same of 4 and 3 is 12 4 trees are 12 minus 3 4s are 12 and 4 into 2 is 8 so this is equal to minus 5 divided by 12 thus on evaluating the given we have to answer as minus 5 divided by 12 so this completes the session bye and take care