There's a problem in my textbook- find the sine,cosine,tangeant, for 105=60+45 (all angles)

I put in the sine of 105 in my calculator and got the same number when I entered the exact answer that I got: √6 +√2/4. The answer they want for the sine of 105 is √2/4(√3+1), and it's in the same format for 30 more questions and I can't figure out how to put it in a different(and more complicated) form. Can someone show me how to convert my answer into the book's answer?