 Hello and welcome to the session. In this session we are going to discuss the following question which says that what is the exact value of sin of 75 degrees minus of sin of 15 degrees. We know that sin of alpha plus beta is equal to sin of alpha into cos of beta plus cos of alpha into sin of beta. Also sin of alpha minus beta is equal to sin of alpha into cos of beta minus of cos of alpha into sin of beta. With this key idea we shall proceed to the solution. In this question we have to find the exact value of sin of 75 degrees minus of sin of 15 degrees and we will make use of sum and difference formula to evaluate it. Here we write each angle in sum or difference form in terms of angles whose table values are known that is 0 degrees, 30 degrees, 45 degrees, 60 degrees or 90 degrees and here we can write 75 degrees as 45 degrees plus 30 degrees. Also we can write 15 degrees as 45 degrees minus 30 degrees. Thus we write sin of 75 degrees minus sin of 15 degrees as sin of 45 degrees plus 30 degrees minus of sin of 45 degrees minus 30 degrees and now using this sum and difference formula we can evaluate this expression. From the key idea we know that sin of alpha plus beta is equal to sin of alpha into cos of beta plus cos of alpha into sin of beta. Also sin of alpha minus beta is equal to sin of alpha into cos of beta minus of cos of alpha into sin of beta. This implies that sin of 75 degrees minus sin of 15 degrees is equal to sin of 45 degrees into cos of 30 degrees plus cos of 45 degrees into sin of 30 degrees. The whole minus of sin of 35 degrees minus 30 degrees can be written as sin of 35 degrees into cos of 30 degrees minus of cos of 35 degrees into sin of 30 degrees the whole. And we know that sin of 45 degrees is equal to 1 upon square root of 2 and cos of 45 degrees is equal to 1 upon square root of 2. Similarly sin of 30 degrees is equal to 1 by 2 and cos of 30 degrees is equal to square root of 3 by 2. Now putting all these values in this expression we get sin of 35 degrees that is 1 upon square root of 2 into cos of 30 degrees that is square root of 3 upon 2 plus cos of 35 degrees that is 1 upon square root of 2 into sin of 30 degrees that is 1 upon 2 the whole minus of sin of 35 degrees that is 1 upon square root of 2 into cos of 30 degrees that is square root of 3 by 2 minus of cos of 35 degrees that is 1 upon square root of 2 into sin of 30 degrees that is 1 by 2 the whole. And this is equal to 1 into square root of 3 that is square root of 3 upon square root of 2 into 2 that is 2 root 2 plus 1 upon 2 root 2 the whole minus of square root of 3 upon 2 into square root of 2 minus of 1 upon 2 into square root of 2 the whole. Now we will open the brackets and we get square root of 3 upon 2 into square root of 2 plus 1 upon 2 into square root of 2 minus of square root of 3 upon 2 into square root of 2 minus of minus of 1 upon 2 into square root of 2 is plus of 1 upon 2 into square root of 2 and this is equal to 1 upon 2 into square root of 2 plus 1 upon 2 into square root of 2. Since the denominator of the two terms is same so the Lcm would be 2 into square root of 2 and we will add the terms in the numerator that is 1 plus 1 and this is equal to 2 upon 2 into square root of 2 which is equal to 1 upon square root of 2 plus sin of 75 degrees minus of sin of 15 degrees is equal to 1 upon square root of 2 which is the required answer. This completes our session. Hope you enjoyed this session.