大师作文网设cos (x +π/4 )＝3/5,17π/12
来源：学生作业帮 编辑：大师作文网作业帮 分类：数学作业 时间：2024/11/12 10:27:55
设cos (x +π/4 )＝3/5,17π/12
∵17π/12sinx+cosx=-4√2/5.(2)
∴由(2)-(1)得2sinx=-7√2/5 ==>sinx=-7√2/10
由(2)+(1)得2cosx=-√2/5 ==>cosx=-√2/10
故(sin2x+2sin²x)/(1-tan x)=(2sinxcosx+2sin²x)/(1-sinx/cosx)
=2sinx(cosx+sinx)/(1-sinx/cosx)
=2(-7√2/10)(-√2/10-7√2/10)/(1-(-7√2/10)/(-√2/10))
=-28/75
∴由(2)-(1)得2sinx=-7√2/5 ==>sinx=-7√2/10
由(2)+(1)得2cosx=-√2/5 ==>cosx=-√2/10
故(sin2x+2sin²x)/(1-tan x)=(2sinxcosx+2sin²x)/(1-sinx/cosx)
=2sinx(cosx+sinx)/(1-sinx/cosx)
=2(-7√2/10)(-√2/10-7√2/10)/(1-(-7√2/10)/(-√2/10))
=-28/75
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