f(x)=(1+sinx+cosx)[sin(x/2)-cos(x/2)]/根号（2+2cosx）

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f(x)=(1+sinx+cosx)[sin(x/2)-cos(x/2)]/根号（2+2cosx）
(1)f(x)的化简形式（最好有过程）

f(x)=(1+sinx+cosx)[sin(x/2)-cos(x/2)]/√（2+2cosx）
=[sin²(x/2)+cos²(x/2)+sinx+cosx][sin(x/2)-cos(x/2)]/[√2（1+cosx）]
=[sin²(x/2)+cos²(x/2)+2sin(x/2)*cos(x/2)+cos²(x/2)-sin²(x/2)][sin(x/2)-cos(x/2)]/[√4*（1+cosx）/2]
=｛[sin(x/2)+cos(x/2)]²+[cos(x/2)+sin(x/2)][cos(x/2)-sin(x/2)]｝[sin(x/2)-cos(x/2)]/[√4*cos²(x/2)]
=｛[sin(x/2)+cos(x/2)][sin(x/2)+cos(x/2）+cos(x/2)-sin(x/2)]｝[sin(x/2)-cos(x/2)]/[√4*cos²(x/2)]
=｛[sin(x/2)+cos(x/2)]*2cos(x/2）｝[sin(x/2)-cos(x/2)]/[2*cos(x/2)]
=｛[sin(x/2)+cos(x/2)][sin(x/2)-cos(x/2)]*2cos(x/2）｝/[2*cos(x/2)]
=[sin(x/2)+cos(x/2)][sin(x/2)-cos(x/2)]
=sin²(x/2)-cos²(x/2)
不明白的地方M我

sinx+cosx/sinx-cosx=2 求sinx/cos^3x +cosx/sin^3x （1）已知sinx+cosx=根号2/2,求sin^4x+cos^4x 已知函数f(x)=2根号3sinx.cosx+cos^2x-sin^2x-1 设f（x）=2cosx.sin（x+π/3)-根号3 sin平方x+sinx.cosx f(x)=(sinx)平方+2根号3sin(x+pai/4)cos(x-pai/4)-(cosx)平方-根号3 已知函数f（x）=[（2根号3sin^2x-sin2x)*cosx/sinx]+1 f(x)=2cos*sin(x+π/3)-^3sin^2x+sinx*cosx 化简：{（1+sinx+cosx)[sin（x/2)-cos(x/2)}/根号下的（2+2cosx）化简sin^4x/sinx-cosx - (sinx+cosx)cos^2x/tan^2x-1 (sin^x/sinx-cosx)-sinx+cosx/tan^2x-1 求证 sin^2x/(sinx-cosx)-(sinx+cosx)/tan^2 x-1=sinx+cosx 已知f(x)=3sin^2x+cos^2x-2sinx*cosx