高中数学必修4 题目如图
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高中数学必修4 题目如图
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![高中数学必修4 题目如图](/uploads/image/z/15782573-29-3.jpg?t=%E9%AB%98%E4%B8%AD%E6%95%B0%E5%AD%A6%E5%BF%85%E4%BF%AE4+%E9%A2%98%E7%9B%AE%E5%A6%82%E5%9B%BE)
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