Question

已知函数f（x）=(sin^2x+cosx+1)/(cosx+1),

Answer 1

1.因为1/cosx，所以cosx不等于0，所以x不等于π/2
kπ
又因为根号2
sin(x－π/4），所以sin(x－π/4）不小于0，kπ小于等于x－π/4小于等于π
kπ，所以π/4
kπ小于等于x小于等于5π/4
kπ
综上所述，x的定义域为[π/4
kπ,π/2
kπ)并上(π/2
kπ,5π/4
kπ]
2.因为a是第二象限的角，且tan
a＝－4/3,所以cos
a=-3/5，sin
a=4/5
又因为f(x)＝1/2cosx-根号2
sin(x－π/4）=1/2cosx-根号2(sinxcosπ/4-cosxsinπ/4)
所以f(a)=1/2(-3/5)-根号2[4/5*二分之根号二-(-3/5)二分之根号二]
=-5/6-根号(2根号2/5
3根号2/10)
=-5/6-根号(0.7根号2)