已知sin(4 π-x)=13分之5 求cos(4 π x)分之cos2x
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1.∵sin[(π/4)-x)]=5/13,0
cos2x/cos[(pi/4)+x]=(cosx-sinx)(cosx+sinx)/[cos(pi/4)cosx-sin(pi/4)sinx=√2(cosx+sinx)=2cos[(pi/4)-x]
f(x)=cos^2x+sinxcosx=(1+cos2x)/2+1/2*sin2x=1/2+1/2(cos2x+sin2x)=√2/2*(√2/2*cos2x+√2/2sin2x)+1/2=√2/2
sin(PI/6+2x)=cos(PI/2-PI/6-2x)=cos(PI/3-2x)=cos(2*(PI/6-x))=1-2*sin(PI/6-x)^2=1-2*(1/4)^2=7/8tan70*c
先用tanx=sinx/cosx、倍角公式、诱导公式化简原函数:f(x)=sin²x+sinxcosx-sin[2(x+π/4)]=(1-cos2x)/2+1/2sin2x-sin(2x+π
2sin(x-π/4)sin(x+π/4)=cos(x-π/4-x-π/4)-cos(x-π/4+x+π/4)=-cos2xf(x)=cos(2x-π/3)-cos2x=cos(2x-π/6-π/6)
/>(1)f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)=cos(2x-π/3)+2sin(x-π/4)cos[π/2-(x+π/4)]=cos(2x-π/3)+2sin
f(x)=sin(2x-π/6)=cos[π/2-(2x-π/6)]=cos(2π/3-2x)=cos(2x-2π/3),故f(x)为偶函数,且其关于x=π/3对称,周期为π,因此a的最小整数为π.
cos2x=sin(π/2-2x)=2sin(π/4-x)cos(π/4-x)cos2x/[sin(π/4-x)]=2sin(π/4-x)cos(π/4-x)/[sin(π/4-x)]=2cos(π/
f(x)=cos(2x-π/3)+2sin(x-π/4)sin(x+π/4)=cos(2x-π/3)+2sin(x-π/4)cos[π/2-(x+π/4)]=cos(2x-π/3)+2sin(x-π/
将函数f(X)=(1+1/tanx)sin^2x+msin(x+π/4)sin(x-π/4)化简得:=(1+cosx/sinx)*2sinxcosx+m(sinxcosπ/4+cosxsinπ/4)(
f(x)=sin^2x+2√3sinxcosx+sin(x+π/4)sin(x-π/4)=(1-cos2x)/2+√3sin2x+(1/2)2sin(x-π/4)cos(x-π/4)=2-2cos2x
f(x)=(1+1/tanx)*(sinx)^2-2sin(x+π/2)sin(x-π/4)=(1+cosx/sinx)*(sinx)^2+2sin(x+π/4)cos[(x-π/4)+π/2]=(s
【参考答案】D[sin(π/2-x)+sin(π-x)]/[cos(-x)+sin(2π-x)]=2009根据诱导公式,化简(cosx+sinx)/(cosx-sinx)=2009左边分子分母同时除以
解析:由已知得:sin(π/4-x)=sin(π/2-π/4-x)=cos(π/4+x)=12/13因为0
利用三角函数积化和差及和差化积公式,f(x)=cos(2x-π/3)-[cos(x-π/4+x+π/2)-cos(x-π/4-x-π/2)]=cos(2x-π/3)-[cos(2x+π/4)-cos(