Question

VERIFY
SinA Sin(60-A) Sin (60+A) = 1/4Sin³A

Answer 1

stick to above reference.

Answer 2

Answer

SinA Sin(60-A) Sin (60+A) = 1/4Sin³A

=>  sin(A) * [sin(60)cosA) - sin(A)cos(60)) * (sin(60)cos(A) + sin(A)cos(60)]

=>  sin(A) * (sin(60)² * cos(A)² - sin(A)² * cos(60)²)

=>  sin(A) * [(3/4) * cos(A)² - (1/4) * sin(A)²]

=>  (1/4) * sin(A) * (3cos(A)² - sin(A)²)

=>  (1/4) * sin(A) * (3 - 3sin(A)² - sin(A)²)

=>   (1/4) * (3sin(A) - 4sin(A)³)

=>   (1/4) * sin³(A)  

Hence

L.H.S = R.H.S (Verified)