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.
Answer & explanation
Correct answer: option 2
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 × \(\frac{\sqrt {3}}{2}\) × \(\frac{\sqrt {3}}{2}\)
⇒ \(\frac{9}{4}\)