 Good morning friends, I am Purva and today we will discuss the following question evaluate without using trigonometric tables 3 into cos 55 degree upon 7 into sine 35 degree minus 4 into cos 70 degree into cosec 20 degree upon 7 into tan 5 degree into tan 25 degree into tan 45 degree into tan 65 degree into tan 85 degree Let us begin with the solution now Now we have to evaluate 3 into cos 55 degrees upon 7 into sine 35 degrees minus 4 into cos 70 degrees into cosec 20 degrees upon 7 into tan 5 degrees into tan 25 degrees into tan 45 degrees into tan 65 degrees into tan 85 degrees Now this is equal to 3 into now we can write cos 55 degrees as cos 90 degree minus 35 degrees upon 7 into sine 35 degrees minus 4 into Now again we can write cos 70 degrees as cos 90 degree minus 20 degree into cosec 20 degrees upon 7 into tan 5 degrees into tan 25 degrees into now tan 45 degrees is equal to 1 so we get into 1 into tan 65 degrees can be written as tan 90 degrees minus 25 degrees into tan 85 degrees can be written as tan 90 degrees minus 5 degrees Now here we write since tan 45 degrees is equal to 1 This is equal to 3 into now we know that cos 90 degree minus theta is equal to sine theta So here we have sine 35 degrees upon 7 into sine 35 degrees minus 4 into now again cos of 90 degrees minus theta is equal to sine theta so we get 4 into sine 20 degrees into cosec 20 degrees upon 7 into tan 5 degrees into tan 25 degrees into now tan of 90 degrees minus theta is equal to cos theta so we get cos 25 degrees into again tan of 90 degrees minus 5 degrees is equal to cot 5 degrees because tan 90 degrees minus theta is equal to cot theta and Here we write since cos 90 degrees minus theta is equal to sine theta and tan 90 degrees minus theta is equal to cot theta Now this is equal to now cancelling out sine 35 degrees in numerator and denominator here We get 3 upon 7 minus 4 upon 7 and this is since sine theta into cosec theta is Equal to 1 so here sine 20 degree into cosec 20 degree is equal to 1 so we get 4 into 1 which is equal to 4 and also tan theta Into cot theta is equal to 1 so here in denominator tan 5 degree into cot 5 degree becomes 1 and tan 25 degrees into cot 25 degree becomes 1 so we get 7 into 1 in denominator which is equal to 7 and This is further equal to minus 1 upon 7 So we have got our answer as minus 1 upon 7. Hope you have understood the solution. Bye and take care