sin(x-π/4 + π/2 )=-cos(x+π/4) 为什么会这样 sin的+π/2 不是会变 cos 为什么会这样啊?主要是不知道那个负号!

2sin(x+π/4)sin(x-π/4)=? 已知sin(π/2-x)+sin(π-x)/cos(-x)+sin(2π-x)=2009,则tan(x+5π/4)等于?已知sin(π/2-x)+sin(π-x)/cos(-x)+sin(2π-x)=2009,则tan(x+5π/4)等于（） A.-2009 B.-1/2009 C.1/2009 D.2009 y=sinx+cosx可化成_____?A.2sin(x-π/4)；B.2sin(x+π/4)； C.√2sin(x-π/4)；D.√2sin(x+π/4)； 求证:(sin 2x /(1-cos 2x) )·(sin x /(1+sin x))=tan (π/4-x/2). 函数f(x)=cos2x+cos(x+π/3)+sin(x+π/6)+3sin^2x的最小值A.0 B.2 C.9/4 D.3 f(x)=（1+cotx)sin^2x-2sin(x+π/4)sin(x-π/4)还有一题, 已知函数f(x)=(1+1 anx)sin^2x+m sin(x+π/4)sin(x-π/4) 已知sin(x+π/6)=1/4,求sin(5π/6-x)+sin^2(π/3-x) sin^2(π/4 +x) 函数f(x)=2sin(x+π/4)sin(x-π/4)+sin2x的值域 求f【x】=2sin[x+π/4]sin[x-π/4]+sin2x的最大值 已知 sinα + cosα / sinα - cosα = 2 ,则 sin(α-5π) x sin(3π/2-α)等于A,3/4B,±3/10C,3/10D,-3/10 求sin^2(2x+π/3)的导数这样写为什么不对：[sin^2(2x+π/3)]'=[sin(2x+π/3)·sin(2x+π/3)]'=2[sin(2x+π/3)]'·sin(2x+π/3)=2cos(2x+π/3)·sin(2x+π/3)=sin(4x+2π/3) f(x)=cos(2x-x/3)+2sin(x-π/4)sin(x+π/4)sin(x+π/4)化简. 化简：2sin(πx/8+π/4)+sin(-πx/8+π/4)= sin(x+π/4) 证明2sin(π/4+x)sin(π/4-x)=cos2x 2sin(x-π/4)sin(x+π/4)=?答案是-cos2x 还是cos2x