Question

函数Y=(1-cosx)/sinx的周期？

Answer 1

1-cosx=2sin^2(x/2)
sinx=2sin(x/2)cos(x/枣竖2)
Y=(1-cosx)/sinx
=tan(x/州岩培2)
tanx周期为π
tan(x/2)周期为π/册唯(1/2)=2π

Answer 2

用万能公式

y=[1-(1-tan²x/2)/(1+tan²岁消镇x/2)]/[2tanx/2/(1+tan²x/2)]
=[2tan²x/桥嫌2/乎粗(1+tan²x/2)]/[2tanx/2/(1+tan²x/2)]
=tan(x/2)
T=π/(1/2)
=2π