Question

show that sin 12° sin 48° sin 54° = 1/8

Answer 1

(sin12° sin48°sin72°sin54°)/sin72°.
now sin(x)sin (60-x )sin (60+x)=1/4 sin 3x
1/4[sin (3×12°)sin54°]/ sin 72°
1/4[sin 36° sin54°]/sin72°
[2×sin36°sin54°]/sin72°×2×4
cos(54-36)/8sin 72°
[cos18°]/8×cos18°
1/8