Question

求下列函数的定义域

（1）y=根号下sinxtanx
(2) y=lgsin2x+根号下9-x^2

Answer 1

sinxtanx>=0
sin^2 x/cosx>=0
则cosx>0
所以是(2kπ-π/2,2kπ+π/2)

sin2x>0
2kπ<2x<2kπ+π
kπ<x<kπ+π/2
9-x^2>=0
-3<=x<=3
所以
[-3,-π/2)∪(0,π/2)

Answer 2

x2+xy/(x+y)2
=x(x+y)/(x+y)2
=x/(x+y)

x2-y2/（x-y）2
=(x+y)(x-y)/(x-y)2
=(x+y)/(x-y)
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