This is another way of getting the answer..I'm afraid i can't explain how the expression can be changed into a double angle form..But I do have a reason for my own working of why the values are the same bur not the sign or placing.Basically,you have to make use of the special angles you know that is equal to the angel inside each trigo function (Sin).Its easier to expand sin(45+60) rather than looking at sin(105) alone..You can't do anything about it but the former helps in expanding using r-formulae..Isn't 45+60=105?.Thats why you have 45+60 & 60-45 where the values are the same..You have learnt the values of special angels so it's easier to do the qn..Hope it helps :)