Question

已知函数f（x）=(sin^2x+cosx+1)/(cosx+1),

Answer 1

1、cosx +1 ≠ 0

cosx ≠ -1

x ≠ (2k+1)π (k∈Z)

2、f(x) = (1-cos²x +cosx+1) / (cosx+1)

= [(2-cosx)(1+cosx)] / (cosx+1)

= 2 - cosx

最小正周期 2π

偶函数