Your clue lies in "b+c=180 degrees", as now c=180-b.

sin(angle) gives the vertical co-ordinate in a circle of radius 1, centre (0,0).

Hence sin(b)=sin(180-b).

Therefore your equation becomes

Using similar logic

allows you to write the entire equation in terms of any one of the four of

sinc, sinb, cosc, cosb

with etc