If A, B, C are angles of a triangle, then find value of sin(B+C).sinA + sin(C+A).sinB + sin(A+B).sinC.

9 \(\frac{9}{4}\) 6 2\(\sqrt {3}\)

\(\frac{9}{4}\)

Let A=B=C=60° ⇒ sin(B+C).sinA + sin(C+A).sinB + sin(A+B).sinC ⇒ sin120°sin60° + sin120°sin60° + sin120°sin60° ⇒ 3 × sin(90°+30°) sin60° ⇒ 3 × cos30°sin60° ⇒ 3 × \(\frac{\sqrt {3}}{2}\) × \(\frac{\sqrt {3}}{2}\)  ⇒ \(\frac{9}{4}\)