Question

Prove that sinA sin(60° - A)sin(60° + A) = 1/4 sin3A

Difficulty level = 2/3

Answer 1

Step-by-step explanation:

Question :

sinAsin(60° - A)sin(60° + A) = 1/4 sin3

Solution :

Considering L.H.S :

⇒ sinAsin(60° - A)sin(60° + A)

∵ sin(A + B)sin(A - B) = sin²A - sin²B

⇒ sinA(3/4 - sin²A)

⇒ 1/4sinA(3 - 4sin²A)

⇒ 1/4(3sinA - 4sin³A)

⇒ 1/4sin3A = R.H.S