Question 963649
Please solve this equation exactly. 
sin(arccos(3/5) - arctan(5/12)) =
***
let reference angle x=arccos(3/5)
cosx=3/5
sinx=4/5
let reference angle y=arctan(5/12)
cosy=12/13
siny=5/13
Identity: sin(x-y)=sinxcosy-cosxsiny=4/5*12/13-3/5*5/13=48/65-15/65=33/65
sin(arccos(3/5) - arctan(5/12)) =33/65
..
Check:
arccos(3/5)≈53.13˚
arctan(5/12)≈22.62˚
53.13-22.62=30.51˚
sin(30.51)≈0.5077
exact value as computed above=33/65≈0.5077