 Hi and welcome to the session. Let us discuss the following question which says without using the trigonometric tables evaluate the following 11 upon 7 into sin 70 degrees upon cos 20 degrees minus 4 upon 7 into cos 53 degrees into cosecant 37 degrees upon tan 15 degrees into tan 35 degrees into tan 55 degrees into tan 75 degrees. Before moving on to the solution let's see the key idea that we will be using for this question. For some angle theta sin 90 degree minus theta is equal to cos theta cosecant 90 degree minus theta is equal to cosecant theta and tan 90 degree minus theta is equal to cot theta. Now let's move on to its solution. We are given 11 upon 7 into sin 70 degrees upon cos 20 degrees minus 4 upon 7 into cos 53 degrees into cosecant 37 degrees upon tan 15 degrees into tan 35 degrees into tan 55 degrees into tan 75 degrees. Now here 70 plus 20 is 90 so we can write 70 as 90 minus 20. So this will be equal to 11 upon 7 into sin 90 degrees minus 20 degrees upon cos 20 degrees minus 4 upon 7 into Now here 53 plus 37 is 90 so we can write 37 as 90 minus 53 so from this we will get cos 53 degrees into cosecant 90 degrees minus 53 degrees upon now here 15 plus 75 is 90 so we can change 75 to 90 minus 15 and 35 plus 55 is 90 so we will change 55 to 90 minus 35 so we get tan 15 degrees into tan 35 degrees into tan 90 degrees minus 35 degrees into tan 90 degrees minus 15 degrees. So this will be equal to 11 upon 7 into cos 20 degrees upon cos 20 degrees. Here we know that sin 90 degrees minus theta is equal to cos theta as we have done in the key idea. So here we get sin 90 degrees minus 20 degrees is equal to cos 20 degrees minus 4 by 7 into cos 53 degrees into secant 53 degrees because cosecant 90 degrees minus theta is equal to secant theta upon tan 15 degrees into tan 35 degrees into cot 35 degrees into cot 15 degrees. Because tan 90 degrees minus theta is equal to cot theta now this will be equal to 11 upon 7 into here cos 20 and cos 20 will get cancelled so we will get 1 minus 4 upon 7 into cos 53 degrees into 1 upon cos 53 degrees as secant theta is equal to 1 upon cos theta upon tan 15 degrees into tan 35 degrees into 1 upon tan 35 degrees into 1 upon tan 15 degrees because cot theta is equal to 1 upon tan theta. So here cos 53 degrees will get cancelled tan 15 degrees will get cancelled and tan 35 degrees will also get cancelled. So we are left with 11 upon 7 minus 4 upon 7 into 1 which gives 11 upon 7 minus 4 upon 7 that is 11 minus 4 upon 7 which is equal to 7 upon 7 that is 1. So 1 is the required answer to this question with this we finish this session hope you must have understood the question goodbye take care and have a nice day.