Question

B-C = (b+c) sin A,Using sin-formula
A 2​

Answer 1

Answer:

have read these formulae in my book but i could not understand how these are proved.

sinA2=(s−b)(s−c)bc−−−−−−−√;sinB2=(s−c)(s−a)ca−−−−−−−√;sinC2=(s−a)(s−b)ab−−−−−−−√ and

cosA2=s(s−a)bc−−−−−√;cosB2=s(s−b)ca−−−−−√;cosC2=s(s−c)ab−−−−−√

where A,B,C are the angles of a triangle ABC and a,b,c are the sides opposite to the angles A,B,C respectively.

I know that area of triangleΔ=12bcsinA

But area of triangle by Heron's formula is Δ=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√

sinA=2Δbc

2sinA2cosA2=2Δbc

sinA2cosA2=s(s−a)(s−b)(s−c)√bc

I do not know how to prove it further or there is some other method to prove it.