百度作业网高中数学必修4 题目如图
来源：学生作业帮 编辑：百度作业网作业帮 分类：数学作业 时间：2024/06/22 23:01:33
高中数学必修4 题目如图
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1.两边平方：(sinx+cosx)^2 = (sinx)^2 + 2sinx*cosx + (cosx)^2 = 1+2sinx*cosx = 1/25
2sinx*cosx=-24/25
(sinx-cosx)^2 =(sinx+cosx)^2 - 4sinx*cosx = (1/25) + (48/25) = 49/25
则：sinx-cosx=±7/5
∵-π/2＜x＜0且sinx+cosx＞0
∴sinx-cosx=-7/5
2.原式=[2sinx*cosx + 2(sinx)^2] / [(cosx/cosx) - (sinx/cosx)]
=[2sinx(cosx+sinx)] / [(cosx-sinx)/cosx]
=[2sinx*cosx*(1/5)] / [-(sinx-cosx)]
=[(-24/25)*(1/5)] / (7/5)
=-24/175
2sinx*cosx=-24/25
(sinx-cosx)^2 =(sinx+cosx)^2 - 4sinx*cosx = (1/25) + (48/25) = 49/25
则：sinx-cosx=±7/5
∵-π/2＜x＜0且sinx+cosx＞0
∴sinx-cosx=-7/5
2.原式=[2sinx*cosx + 2(sinx)^2] / [(cosx/cosx) - (sinx/cosx)]
=[2sinx(cosx+sinx)] / [(cosx-sinx)/cosx]
=[2sinx*cosx*(1/5)] / [-(sinx-cosx)]
=[(-24/25)*(1/5)] / (7/5)
=-24/175