为天添翼
幼苗
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向量m.向量n=2√2cosa+cosasina+2√2sina-sinacosa.
=2√2(sina+cosa)=1.
=2√2*√2sin(a+π/4)=1.
∴sin(a+π/4)=1/4.
cos(a+7π/12)=cos(a+π/4+π/3).
=cos(a+π/4)cosπ/3-sin(a+π/4)sinπ/3.
=(√15/4)*(1/2)-(1/4)*√3/2.【cos(a+π/4)=√[1-sin^2(a+π/4)]=√15/4】
=(√3/8)(√5-1)
∴cos(a+7π/12)=(√3/8)(√5-1).
1年前
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