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化简:sin(π/8)Cos(π/8)=?

详细步骤写在纸上了

sin平方22.5度 =(1-cos45度)/2 =(2-根2)/4 sin22.5度 =根下(2-根2)/2

sin8/π*cos8/π=1/2sin4/π=四分之根号2

f(x)= 2cos(x-π/3)+2sin(3π/2-x) =2cos(x-π/3)-2cosx =2(cosxcosπ/3+sinxsinπ/3)-2cosx =√3sinx+cosx-2cosx =√3sinx-cosx =2(sinxcosπ/6-cosxsinπ/6) =2sin(x-π/6)

sin105°-cos105° =√2(sin105°cos45°-cos105°sin45°) =√2sin(105°-45°) =√2sin60° =√2*√3/2 =√6/2 (cosπ/12+sinπ/12)(cosπ/12-sinπ/12) =cos²π/12-sin²π/12 =cosπ/6 =√3/2 1-2sin²π/8 =cos(π/4) =√2/2

-cos(π/16)sin(π/16)cos(π/8) =(-1/2)·2cos(π/16)sin(π/16)cos(π/8) =(-1/2)·sin(π/8)cos(π/8) =(-1/4)·2sin(π/8)cos(π/8) =(-1/4)·sin(π/4) =(-1/4)·(√2/2) =-√2/8。

sin(πx/4-π/6)=sinπx/4cosπ/6-cosπx/4sinπ/6=√3/2*sinπx/4-1/2*cosπx/4 2cosπx/8=2*(1+cosπx/4)/2=1+cosπx/4 ∴f(x)=(√3/2*sinπx/4-1/2*cosπx/4)-(1+cosπx/4)+1=√3/2*sinπx/4-3/2cosπx/4 =√3(1/2*sinπx/4-√3/2cosπx/4) =√3(cosπ/3*sinπx/4-sinπ/...

最基本的是两角和的公式,延伸的是倍角公式。

1/16。 解:cosπ/9×cos2π/9×cos3π/9×cos4π/9 =(2sinπ/9xcosπ/9×cos2π/9×cos3π/9×cos4π/9)/2sinπ/9 =(sin2π/9xcos2π/9×cos3π/9×cos4π/9)/2sinπ/9 =(2sin2π/9xcos2π/9×cos3π/9×cos4π/9)/4sinπ/9 =(sin4π/9xcos3π/9×cos4π/9)/4sinπ/9 =(sin4π/9×cos...

f(x)=sin(wx+φ)+cos(wx+φ)=√2sin(wx+φ+π/4)T=2π/w=πw=2f(x)=√2sin(2x+φ+π/4)f(-x)=f(x),所以f(-π/8)=f(π/8)sinφ=sin(π/2+φ)=cosφtanφ=1|φ|

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