求y=lg(sinx-cosx)的定义域 - 知识问答

求y=lg(sinx-cosx)的定义域

2个回答

真数sinx-cosx＞0
sinx-cosx
=√2（√2/2sinx-√2/2cosx)
=√2(sinxcosπ/4-cosxsinπ/4)
=√2sin(x-π/4)＞0
2kπ＜x-π/4＜2kπ+π
2kπ+π/4＜x＜2kπ+π5/4
因此定义域为(2kπ+π/4,2kπ+5/4π)

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