I'm not strong with this, i need some help:
2(1-sin(b)sin(c)) = cos^2(b) + cos^(c) when b+c = 180
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