sin6°sin42°sin66°sin78°求值
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解：原式=sin6°cos12°cos24°cos48°
=8cos6°sin6°cos12°cos24°cos48°/8cos6°
=4sin12°cos12°cos24°cos48°/8cos6°
=2sin24°cos24°cos48°/8cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=sin6°/16cos6°
=1/16
答：原式的值为1/16
=8cos6°sin6°cos12°cos24°cos48°/8cos6°
=4sin12°cos12°cos24°cos48°/8cos6°
=2sin24°cos24°cos48°/8cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=sin6°/16cos6°
=1/16
答：原式的值为1/16
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sin6°sin42°sin66°sin78°
=sin6°cos12°cos24°cos48°
=8cos6°sin6°cos12°cos24°cos48°/8cos6°
=4sin12°cos12°cos24°cos48°/8cos6°
=2sin24°cos24°cos48°/8cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=sin6°/16cos6°
=1/16
=sin6°cos12°cos24°cos48°
=8cos6°sin6°cos12°cos24°cos48°/8cos6°
=4sin12°cos12°cos24°cos48°/8cos6°
=2sin24°cos24°cos48°/8cos6°
=sin48°cos48°/8cos6°
=sin96°/16cos6°
=sin6°/16cos6°
=1/16
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sin6°sin42°sin66°sin78°
=sin6°cos12°cos24°cos48°
=16cos6°sin6°cos12°cos24°cos48°/16cos6°
=8sin12°cos12°cos24°cos48°/16cos6°
=4sin24°cos24°cos48°/16cos6°
=2sin48°cos48°/16cos6°
=sin96°/16cos6°
=cos6°/16cos6°
=1/16
=sin6°cos12°cos24°cos48°
=16cos6°sin6°cos12°cos24°cos48°/16cos6°
=8sin12°cos12°cos24°cos48°/16cos6°
=4sin24°cos24°cos48°/16cos6°
=2sin48°cos48°/16cos6°
=sin96°/16cos6°
=cos6°/16cos6°
=1/16
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