1 已知 cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4),求sin(α+β)的值2 已知α,β都是锐角,tanα=1/7,sinβ=根号10/10,求tan(α+2β)的值3 已知函数y=(sinx+cosx)^2+2cos^2x,(1)求它的递减区间?(2)求
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![1 已知 cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4),求sin(α+β)的值2 已知α,β都是锐角,tanα=1/7,sinβ=根号10/10,求tan(α+2β)的值3 已知函数y=(sinx+cosx)^2+2cos^2x,(1)求它的递减区间?(2)求](/uploads/image/z/2615634-18-4.jpg?t=1+%E5%B7%B2%E7%9F%A5+cos%28%CF%80%2F4-%CE%B1%29%3D3%2F5%2Csin%285%CF%80%2F4%2B%CE%B2%29%3D-12%2F13%2C%CE%B1%E2%88%88%28%CF%80%2F4%2C3%CF%80%2F4%29%2C%CE%B2%E2%88%88%280%2C%CF%80%2F4%29%2C%E6%B1%82sin%28%CE%B1%2B%CE%B2%29%E7%9A%84%E5%80%BC2+%E5%B7%B2%E7%9F%A5%CE%B1%2C%CE%B2%E9%83%BD%E6%98%AF%E9%94%90%E8%A7%92%2Ctan%CE%B1%3D1%2F7%2Csin%CE%B2%3D%E6%A0%B9%E5%8F%B710%2F10%2C%E6%B1%82tan%28%CE%B1%2B2%CE%B2%29%E7%9A%84%E5%80%BC3+%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0y%3D%28sinx%2Bcosx%29%5E2%2B2cos%5E2x%2C%EF%BC%881%EF%BC%89%E6%B1%82%E5%AE%83%E7%9A%84%E9%80%92%E5%87%8F%E5%8C%BA%E9%97%B4%3F%EF%BC%882%EF%BC%89%E6%B1%82)
1 已知 cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4),求sin(α+β)的值2 已知α,β都是锐角,tanα=1/7,sinβ=根号10/10,求tan(α+2β)的值3 已知函数y=(sinx+cosx)^2+2cos^2x,(1)求它的递减区间?(2)求
1 已知 cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4),求sin(α+β)的值
2 已知α,β都是锐角,tanα=1/7,sinβ=根号10/10,求tan(α+2β)的值
3 已知函数y=(sinx+cosx)^2+2cos^2x,
(1)求它的递减区间?
(2)求它的最大值和最小值?
1楼跟3楼瞧不起人啊,不懂就要问没听过吗
1 已知 cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4),求sin(α+β)的值2 已知α,β都是锐角,tanα=1/7,sinβ=根号10/10,求tan(α+2β)的值3 已知函数y=(sinx+cosx)^2+2cos^2x,(1)求它的递减区间?(2)求
1.sin(α+β)=-sin[(5π/4+β)-(π/4-α)]=-sin(5π/4+β)*cos(π/4-α)+cos(5π/4+β)*sin(π/4-α)
由:α∈(π/4,3π/4),β∈(0,π/4)得 (π/4-α)∈(-π/2,0),(5π/4+β)∈(5π/4,3π/2)
从而 sin(π/4-α)=-4/5,cos(5π/4+β)=-5/13 代入第一式 =-(-12/13)*3/5+(-5/13)*(-4/5)=56/65
2.α,β都是锐角,tanβ=sinβ/cosβ=(根号10/10)/(3根号10/10)=1/3,得 tan(α+2β)=tan[(α+β)+β]
tan[(α+β)+β]=(tan(α+β)+tanβ)/(1-tan(α+β)*tanβ)
又 tan(α+β)=(tanα+tanβ)/(1-tanα*tanβ)=1/2 代入上式
得 tan(α+2β)=tan[(α+β)+β]=1
3.
y=(sinx+cosx)^2+2cos^2x=cos^2x+sin^2x+2sinx*cosx+2cos^2x
也就等于 =1+2sinx*cosx+2cos^2x=1+2sinx*cosx+cos(2x)+1
=1+sin(2x)+cos(2x)+1=2+根号2sin(2x+π/4)
sin函数 减区间为 (2kπ+π/2)