Applying sum identity

Question

What is the correct way to apply the Sum Identity to find sin105°?

Answer 1

There is more than one way, but one possibility is:

sin105° = sin(45° + 60°)

= sin45°cos60° + cos45°sin60°

= (√2/2)(1/2) + (√2/2)(√3/2) = (√2 + √6) / 4