Question

sinA/sin(A+B)=a/c prove

Answer 1

a/sinA=b/sinB=c/sinC=2R

so, a=2RsinA

c=2RsinC

solving L.H.S.

»a/c

»2RsinA/2RsinC

»sinA/sinC

»sinA/sin(180-C) (because sin(180-x)=sinx)

»sinA/sin(A+B)=RHS

because A+B+C=180

SO 180-C=A+B

Answer 2

Answer:

a/sinA=b/sinB=c/sinC=2R

so, a=2RsinA

c=2RsinC

solving rhs

»a/c

»2RsinA/2RsinC

»sinA/sinC

»sinA/sin(180-C) (because sin(180-x)=sinx)

»sinA/sin(A+B)=RHS

because A+B+C=180

SO 180-C=A+B