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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。

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

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...

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

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...

恒等式:sin(x)=cos(90°-x)

解:sin(6°)*sin(42°)*sin(66°)*sin(78°) =[sin(12°)sin(84°)sin(132°)sin(156°)]/[16cos(6°)cos(42°)cos(66°)cos(78°)] (分子分母同乘16cos(6°)cos(42°)cos(66°)cos(78°),并应用正弦倍角公式) =[cos(78°)cos(6°)cos(42°)cos(66°)]/[16cos(6°)c...

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°...

sin6ºsin42ºsin66ºsin78º =sin6º*cos12º*cos24º*cos48º =2cos6º*sin6º*cos12º*cos24º*cos48º/2cos6º =sin12º*cos12º*cos24º*cos48º/2cos6º =2...

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