sin12° sin 24° .sin 48° . sin84 =
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sin12. sin24. sin48. sin84
⇒1/4*(2sin84 sin24) (2sin48 sin12)
⇒ 1/4*(cos60- cos108)(cos36- cos60)
⇒ 1/4*(1/2 + sin18) (cos36 - 1/2)
⇒1/4*(1/2 + (root5 - 1)/4) ((root5 + 1)/4 - 1/2)
⇒1/4* ((root5 + 1)/4) ((root5 - 1)/4)
⇒ 1/6*4 * (5-1)
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