sin(2x-π/2)=-cos2x是怎么来的,

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如图单位长度为半径的圆,假定OA与x轴正半轴的夹角是2x,则2x-π/2就是与之垂直的OA'与x轴正半轴的夹角（顺时针旋转90度）.sin2x是A的纵坐标,cos2x是A的横坐标sin(2x-π/2) 是A'的纵坐标,数值上等...

cos[π/2-πx/2]=sinπx/2.这是怎么变来的.
若sin(x-π)=2cos(2π-x),求(sin(π-x)+5cos(2π-x))/(3cos(π-x)-sin(-
(1-cos2x)+sin2x=根号2(sin2x cosπ/4-cos2x sinπ/4)+1 这个是怎么化简得的?
f(x)sinx·sin(π-x)+√3sin(π/2+x)cos(π/2+x)+2cos(π+x)cos(π-x) 求
√2sin(x/2+π/4)cos(x/2)=√2/2sin(x+π/4)+ 1/2 怎么得到的
已知f(x)＝sin(x−3π)•cos(2π−x)•sin(−x+3π2)cos(−x−π)•cos(π2−x)
求函数y=[sin2x+sin(2x+π/3)-cos1/2﹙π-4x﹚]/[cos2x+cos﹙2x+π/3﹚-sin
f(x)=1-2sin^2(x+π/8)+2sin(x+π/8)*cos(x+π/8)=cos(2x+π/4)+sin(
(1-cos2x)+sin2x=根号2(sin2x cosπ/4-cos2x sinπ/4)+1
cos2x-sin2x=√2cos（2x+π/4）是怎么来的?太久没练习函数,全都忘了