Sorry if my post is a bit messy, it's my first

Question:

Use an appropriate compound angle formula to express as a single trigonometric function, and then determine an exact value of each.

a) sin(5pi/12)cos(pi/4) + cos(5pi/12)sin(pi/4)

So this is the work i've attempted to do so far, I may be completely wrong and once again I apologize for not knowing how to make the pi symbol

:

sin(x+y) = sinx cosy + cosxsiny

sin(5pi/12 + pi/4) = sin(5pi/12)cos(pi/4) + cos(5pi/12)sin(pi/4)

sin(5pi/12 + 3pi/12) = sin(pi/4 + pi/6)cos(pi/4) + cos(pi/4 + pi/6)sin(pi/4)

***Broke 5pi/12 into pi/4 + pi/6***
sin(8pi/12) = (sin(pi/4) + sin(pi/6))(cos(pi/4)) + (cos(pi/4) + cos(pi/6)(sin(pi/4))

sin(2pi/3) = (1/sqr2 + 1/2)(1/sqr2) + (1/sqr2 + sqr3/2)(1/sqr2)

sqr3/2 =

sqr3/2 = (1 + 1/2) + (1 + sqr3/2)

I'm not entirely sure how to cancel stuff out etc. there, and I would like to know if i'm even doing it right. The answer in the back of textbook is

**sin(5pi/12 + pi/4); sqr3/2**