函数y=(cos x+sin x)/(cos x-sin x)的最小正周期是多少?A.1 B π/2 C 2π D π

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函数y=(cos x+sin x)/(cos x-sin x)的最小正周期是多少?A.1 B π/2 C 2π D π
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函数y=(cos x+sin x)/(cos x-sin x)的最小正周期是多少?A.1 B π/2 C 2π D π
函数y=(cos x+sin x)/(cos x-sin x)的最小正周期是多少?
A.1 B π/2 C 2π D π

函数y=(cos x+sin x)/(cos x-sin x)的最小正周期是多少?A.1 B π/2 C 2π D π
y=(cos x+sin x)/(cos x-sin x)
y=(根号2/2 cosx + 根号2/2 sinx)/(根号2/2 cosx - 根号2/2 sinx)
y=sin(π/4+x)/cos(π/4+x)
y=tan(π/4+x)
选D

y=(cos x+sin x)/(cos x-sin x)
=(cosx+sinx)^2/(cosx^2-sinx^2)
=(1+sin2x)/(1-sinx^2-sinx^2)
=(1+sin2x)/(1-2sinx^2)
=(1+sin2x)/cos2x
=tan2x+1/cos2x
=f(x)

f(x+p)=tan(2x+2p)+1/cos(2x+2p)=tan2x+1/cos2x=f(x)
周期为p
(p代表π)