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sin66

sin6°sin42°sin66°sin78° =(2sin6°cos6°sin42°sin66°sin78°)/(2cos6°) =(2sin12°cos12°sin42°sin66°)/(4cos6°) =(2sin24°cos24°sin42°)/(8cos6°) =(2sin48°cos48°)/(16cos6°) =sin96°/(16cos6°) =cos6°/(16cos6°) =1/16。

Sin6sin42sin66sin78 =Sin6*cos12*cos24*cos48 =2cos6*Sin6*cos12*cos24*cos48/2cos6 =sin12*cos12*cos24*cos48/2cos6 =2sin12*cos12*cos24*cos48/4cos6 =sin24*cos24*cos48/4cos6 =2sin24*cos24*cos48/8cos6 =sin48**cos48/8cos6 =2sin48**cos4...

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 我是老师 谢谢采纳

sin6°sin42°sin66°sin78° =(1/2)·(1/cos6°)·2sin6°cos6°·sin42°sin66°·cos12° =(1/4)·(1/cos6°)·2sin12°cos12°·sin42°·cos24° =(1/8)·(1/cos6°)·2sin24°cos24°·sin42° =(1/16)·(1/cos6°)·2sin42°cos42° =(1/16)·(sin84°/cos6°) =(1/16)·(c...

sin81.8º=0.98978 sin66.2º=0.91496 sin32º=0.52992 代入算式,一算便知。

恒等式:sin(x)=cos(90°-x)

sin6sin42sin66sin78 =sin6(sin78=cos12)(sin78=cos24)(sin42=cos48) =sin6cos12*cos24cos48 =sin6cos6cos12*cos24cos48/cos6 =1/(2sin6cos61/2*2cos12*1cos24*2cos48/cos6 =1/2*1/2sin12*2cos12*cos24*cos48/cos6 =1/4*1/2sin24*cos24*cos48/co...

sin6sin42sin66sin78 =sin6cos48cos24cos12 =2sin6cos6cos12cos24cos48/2cos6 =sin12cos12cos24cos48/2cos6 =sin24cos24cos48/4cos6 =sin48cos48/8cos6 =sin96/16cos6 =cos6/16cos6 =1/16

解: sin60°sin42°sin66°sin78° =sin60°cos48°cos24°cos12° =sin60°cos48°cos24°cos12°sin12°/sin12° =1/2·sin60°cos48°cos24° sin24°/sin12° =1/4·sin60°cos48° sin48°/sin12° =1/8·sin60° sin96°/sin12° =1/8·sin60° cos6°/sin12° =1/8·sin60°...

Sin66°30′20〃=0.9171

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