sin(α+β)sin(α-β)=1/3 求证:1/4(sin2α)^2+(sinβ)^2+(cosα)^4 的定值我是照着题抄下来的,一个是证明吧
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![sin(α+β)sin(α-β)=1/3 求证:1/4(sin2α)^2+(sinβ)^2+(cosα)^4 的定值我是照着题抄下来的,一个是证明吧](/uploads/image/z/6886254-30-4.jpg?t=sin%EF%BC%88%CE%B1%2B%CE%B2%EF%BC%89sin%EF%BC%88%CE%B1-%CE%B2%EF%BC%89%3D1%2F3+%E6%B1%82%E8%AF%81%EF%BC%9A1%2F4%EF%BC%88sin2%CE%B1%EF%BC%89%5E2%2B%EF%BC%88sin%CE%B2%EF%BC%89%5E2%2B%EF%BC%88cos%CE%B1%EF%BC%89%5E4+%E7%9A%84%E5%AE%9A%E5%80%BC%E6%88%91%E6%98%AF%E7%85%A7%E7%9D%80%E9%A2%98%E6%8A%84%E4%B8%8B%E6%9D%A5%E7%9A%84%EF%BC%8C%E4%B8%80%E4%B8%AA%E6%98%AF%E8%AF%81%E6%98%8E%E5%90%A7)
sin(α+β)sin(α-β)=1/3 求证:1/4(sin2α)^2+(sinβ)^2+(cosα)^4 的定值我是照着题抄下来的,一个是证明吧
sin(α+β)sin(α-β)=1/3 求证:1/4(sin2α)^2+(sinβ)^2+(cosα)^4 的定值
我是照着题抄下来的,一个是证明吧
sin(α+β)sin(α-β)=1/3 求证:1/4(sin2α)^2+(sinβ)^2+(cosα)^4 的定值我是照着题抄下来的,一个是证明吧
1/4(sin2α)^2+(sinβ)^2+(cosα)^4
=(sinαcosα)^2+(sinβ)^2+(cosα)^2*(cosα)^2
=(cosα)^2[(sinα)^2+(cosα)^2]+(sinβ)^2
=(cosα)^2+(sinβ)^2=M
cos(a-b)-cos(a+b)=2sinasinb
2/3=2sin(α+β)sin(α-β)=cos(2β)-cos(2α)=1-2(sinβ)^2+1-2(cosα)^2=2-2M
M=2/3
是证明“是定值”,还是求出该定值
2/3
1/4(sin2α)^2+(sinβ)^2+(cosα)^4
=(sinα)^2(cosα)^2+(cosα)^4+(sinβ)^2
=(cosα)^2+(sinβ)^2
我已经有思路了 分我拿定了··
参考这个积化和差公式:
sinα·sinβ=-(1/2)[cos(α+β)-cos(α-β)]
sin(α+β)sin(α-β)=-1/2(cos2...
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1/4(sin2α)^2+(sinβ)^2+(cosα)^4
=(sinα)^2(cosα)^2+(cosα)^4+(sinβ)^2
=(cosα)^2+(sinβ)^2
我已经有思路了 分我拿定了··
参考这个积化和差公式:
sinα·sinβ=-(1/2)[cos(α+β)-cos(α-β)]
sin(α+β)sin(α-β)=-1/2(cos2α-cos2β)=1/3
cos2α-cos2β=-2/3=1-2(sinβ)^2+1-2(cosα)^2
所以(cosα)^2+(sinβ)^2 =(-2/3-2)/-2=2/3
···无语 才算出来
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