sinA . sin(60-A) . sin(60+A) = 1/4 sin3A
sinA . sin(60 – A) . sin(60 + A)
= sinA . (sin60 cos A – cos60 sin A) . (sin60 cos A + cos60 sin A)
= sinA . (sin260 cos2A – cos260 sin2A)
= sinA . {(3/4) cos2A – (1/4) sin2A)
= sinA . {(3/4) – (3/4) sin2A – (1/4) sin2A)
= sinA .{(3/4) – sin2A)
= (3/4) sinA – sin3A
= 1/4 (3 sinA – 4sin3A)
=1/4 sin3A