Question

已知0＜x＜2π,若根号下(1-Sin2x)=Sinx-Cosx,则x的取值范围是?

Answer 1

答案:x=π/4,x=5π/4,x=0,x=π/2

由(1-sin2x)=sinx-cosx得

(sinx-cosx)^2=sinx-cosx

(sinx-cosx)(sinx+cosx-1)=0,故得

sinx-cosx=0或sinx+cosx-1=0

由sinx-cosx=0得

tanx=1,x=π/4,x=5π/4,

由sinx+cosx-1=0得

√2sin(x+π/4)=1

sin(x+π/4)=√2/2

x+π/4=π/4或x+π/4=3π/4

x=0或x=π/2