Question -
Answer -
By using the sine rule we know,
So, c = k sin C
Similarly, a = k sin A
And b = k sin B
We know,
Now let us consider LHS:
b sin B – c sin C
Substituting the values of b and c in the aboveequation, we get
k sin B sin B – k sin C sin C = k (sin2 B– sin2 C) ……….(i)
We know,
Sin2 B – sin2 C = sin(B + C) sin (B – C),
Substituting the above values in equation (i), we get
k (sin2 B – sin2 C) =k (sin (B + C) sin (B – C)) [since, π = A + B + C ⇒ B + C = π –A]
The above equation becomes,
= k (sin (π –A) sin (B – C)) [since, sin (π – θ) = sinθ]
= k (sin (A) sin (B – C))
From sine rule, a = k sin A, so the above equationbecomes,
= a sin (B – C)
= RHS
Hence proved.