Investigate and make a conjecture:

b(cosC) + c(cosB) = ???

Try making your own GSP sketch to investigate, or just click here (requires GSP 4.0):

Try proving this conjecture on your own first, then click here to compare your efforts with this proof:

Extension: Use this theorem and the Law of Sines to deduce the "addition formula": sin(B + C) = sinBcosC + sinCcosB. Try this on your own, then compare your efforts with this.