sinx-cosx=(根号3)/3,则cos(π/2-2x)=?

Question

sinx-cosx=(根号3)/3,则cos(π/2-2x)=?

Answer 1

cos(π/2-2x)=sin2x,sinx-cosx=√3/3,两边同时平方,(sinx)^2-2sinxcosx+(cosx)^2=1/3,
1-sin2x=1/3,sin2x=2/3,
cos(π/2-2x)=sin2x=2/3.