化简sinπ 6 根号3cosπ 6

根号3×cosπ／12－sinπ／12=2(根号三/2cosπ／12-1/2sinπ／12)＝2（sinπ/3cosπ/12-cosπ/3sinπ/12）＝2sin（π/3-π/12）＝根号2

cos(α-π/6)+sinα=cosα*√3/2+1/2*sinα+sinα=cosα*√3/2+3/2*sinα=√3(sinπ/6cosα+cosπ/6sinα)=√3sin(π/6+α)=4/

2sin^2[(π/4)+x]+根号3（sin^x-cos^x）-1=-(1-2sin^2[(π/4)+x)-√3cos2x=-cos(π/2+2x)-√3cos2x=sin2x-√3cos2x=2[

用辅助角公式原式=2(1/2sinπ/12-（根号3）/2cosπ/12)=2(cosπ/3sinπ/12-sinπ/3cosπ/12)=2[sin(π/12-π/3)]=-2(sinπ/4)=-2*

原式=2(cosπ/12*1/2+sinπ/12*√3/2)=2(cosπ/12cosπ/3+sinπ/12sinπ/3)=2cos(π/3-π/12)=2sinπ/4=2×√2/2=√2

原式=2[1/2*c0s(π/6-x)-√3/2*sin(π/6-x)]=2[cos(π/6-x)cosπ/3-sin(π/6-x)sinπ/3]=2cos(π/6-x+π/3)=2cos(π/2-x

解cos(4π/3+a)=cos(π+π/3+a)=-cos(π/3+a)=-cos[π/2-(π/6-a)]=-sin(π/6-a)=-√3/3

cos(α-π/6)+sinα=4√3/5cos(α-π/6)+cos(π/2-α)=4√3/52cos{[(α-π/6)+(π/2-α)]/2}*cos{[(α-π/6)-(π/2-α)]/2}=4

根号3sin(π/6-a)-cos(π/6-a)=2[sin(π/6-a)*cosπ/6-sinπ/6*cos(π/6-a)]=2sin(π/6-a-π/6)=2sin(-a)=-2sina

右边2sin(π/6+A)=2sin(π/6)cosA+2sinAcos(π/6)=cosA+根号3sin(A)=左式.得证#

√2/4sin（π/4-x）+√6/4cos（π/4-x）=√2/2[1/2sin（π/4-x）+√3/2cos（π/4-x）]=√2/2[cosπ/3sin（π/4-x）+sinπ/3cos（π/4

y＝（√3/2）sin（x＋π/2）＋cos（π/6－x）＝（√3/2）cosx＋cos（π/6）cosx＋sin（π/6）sinx＝（√3/2）cosx＋（√3/2）cosx＋（1/2）sinx＝√

√[1-2sin(3-π)cos(3-π)]=√[sin²(3-π)+cos²(3-π)-2sin(3-π)cos(3-π)]=√[sin(3-π)-cos(3-π)]²

应该是你打错了吧?!原式应该是cos(π/3+a)+sin(π/6+a)=cosπ/3cosa-sinπ/3sina+sinπ/6cosa+cosπ/6sina=cosa/2-(根号3)/2sina+

原式=(1/2)cosa-(√3/2)sina+(1/2)cosa+(√3/2)sina=cosa

tanθ=√3/3,θ=kπ+π/6,k为偶数时cos^2θ-sin(θ+π/6)cosθ=3/4-√3/2*√3/2=0k为奇数时cos^2θ-sin(θ+π/6)cosθ=3/4-3/4=0

√3；cosπ/6=√3/2,sinπ/6=1/2所以cosπ/6+√3sinπ/6=√3/2+√3/2=√3希望对你有帮助

cos(5π/6+x)-sin^2(x-π/6）=cos〔π-(π/6-x)〕-〔1-cos^2(x-π/6)〕=-cos(π/6-x)-〔1-cos^2(x-π/6)〕=-cos(π/6-x)-〔1

1sin²α+cosαcos(π/3+α)-sin²(π/6-α)=sin²α+cosα(cosπ/3cosα-sinπ/3sina)-(sinπ/6cosα-cosπ/