y=1-sin(2x)/sin(x)-cos(x)求T.最值

y=1-sin(2x)/sin(x)-cos(x)求T.最值
y=1-sin(2x)/sin(x)-cos(x)求T.最值

y=1-sin(2x)/sin(x)-cos(x)求T.最值
y = { 1-sin(2x) } / { sin(x)-cos(x) }
= { (sinx)^2+(cosx)^2-2sinxcosx } / { sin(x)-cos(x) }
= (sinx - cosx)^2 / { sin(x)-cos(x) }
= sinx - cosx
= 根号2(sinxcosπ/4 - cosxsinπ/4)
= 根号2sin(x-π/4)
T=2π
最小值-根号2
最大值根号2

y=1-sin(2x)/sin(x)-cos(x)=1-y=1-2cos(x)sin(x)/sin(x)-cos(x)=1-3cosx,所以最小T=2π

1-sin2x
=sin²x+cos²x-2sinxcosx
=(sinx-cosx)²
所以y=sinx-cosx
=√2(√2/2*sinx-√2/2cosx)
=√2(sinxcosπ/4-cosxsinπ/4)
=√2sin(x-π/4)
所以最大值=√2，最小值=-√2

sin2x=2sinxcosx
cosx=[-1,1]
T=[-2,4]