Question

a-b/c - sin (A-B/2) /
cos (c/2)

Answer 1

From sine law, we have, asinA=bsinB=csinC=k

So, a=ksinA,b=ksinB,c=ksinC

∴L.H.S.=a−bc=k(sinA−sinB)ksinC

=sinA−sinBsinC

=2sin(A−B2)cos(A+B2)2sin(C2)cos(C2)

Here, A+B+C=180.So,A+B=180−C

So, our expression becomes,

=sin(A−B2)cos(180−C2)sin(C2)cos(C2)

=sin(A−B2)cos(90−C2)sin(C2)cos(C2)

=sin(A−B2)sin(C2)sin(C2)cos(C2)

=sin(A−B2)cos(C2)=R.H.S.