Question

plz answer this que given in picture
we anybody knows how to do it

Answer 1

Answer:

The answer is given below.

Step-by-step explanation:

Use sine formula ,

$\bold{\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}=k}$

∴sinA = ak

sinB = bk

sinC = ck

Also sin(A - B) = sinA.cosB - cosA.sinB

                    = akcosB - cosA.bk

                    = K(acosB - bcosA}

Similarly, sin(B - C) = k(bcosC - ccosB)

sin(C - A) = k(ccosA - acosC)

LHS = asin(B- C) + bsin(C - A) + csin(A - B)

       = ak(bcosC - ccosB) + bk(acosC - ccosA) + ck(acosB - bcosA)

        = k(bccosA - bccosA) + k(accosB - accosB) + k(abcosC - abcosC)

        = 0 + 0 + 0 = 0 = RHS