trig question (1 Viewer)

[Satiric]

In any triangle ABC, write a relationship between the angle A and the sum of the angles B and C. Thus prove, that in triangle ABC
sin A = Sin B cos C + cos B sin C
Deduce that
a = b cos c + c cos b

I get the first part pretty easy, i don't know what they want for the second bit.
can anyone help?
thanks a lot.

This question is from couchman and jones (exercise 24.1 Q10a)

 

[lolokay]

second bit is just sine rule

 

[Trebla]

(sin A)/a = (sin B)/b => sin B = b(sin A)/a
(sin A)/a = (sin C)/c => sin C = c(sin A)/a

sin A = sin B cos C + cos B sin C
sin A = [b(sin A)/a] cos C + cos B [c(sin A)/a]
asin A = sin A(b cos C + c cos B)
a = b cos C + c cos B