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

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