已知sin(a+b)sin(a-b)=1/3,求证:1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa为定值.我不会打平方和四次方,只好搞成相乘了~我做的求证的那堆东东等于cosa.cosa+sinb.sinb.前面的推出:(sinacosb+cosasinb)(sinacosb-
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![已知sin(a+b)sin(a-b)=1/3,求证:1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa为定值.我不会打平方和四次方,只好搞成相乘了~我做的求证的那堆东东等于cosa.cosa+sinb.sinb.前面的推出:(sinacosb+cosasinb)(sinacosb-](/uploads/image/z/7041113-17-3.jpg?t=%E5%B7%B2%E7%9F%A5sin%28a%2Bb%29sin%28a-b%29%3D1%2F3%2C%E6%B1%82%E8%AF%81%EF%BC%9A1%2F4sin2a%EF%BC%8Esin2a%2Bsinb.sinb%2Bcosa.cosa.cosa.cosa%E4%B8%BA%E5%AE%9A%E5%80%BC%EF%BC%8E%E6%88%91%E4%B8%8D%E4%BC%9A%E6%89%93%E5%B9%B3%E6%96%B9%E5%92%8C%E5%9B%9B%E6%AC%A1%E6%96%B9%2C%E5%8F%AA%E5%A5%BD%E6%90%9E%E6%88%90%E7%9B%B8%E4%B9%98%E4%BA%86%7E%E6%88%91%E5%81%9A%E7%9A%84%E6%B1%82%E8%AF%81%E7%9A%84%E9%82%A3%E5%A0%86%E4%B8%9C%E4%B8%9C%E7%AD%89%E4%BA%8Ecosa.cosa%2Bsinb.sinb.%E5%89%8D%E9%9D%A2%E7%9A%84%E6%8E%A8%E5%87%BA%EF%BC%9A%28sinacosb%2Bcosasinb%29%28sinacosb-)
已知sin(a+b)sin(a-b)=1/3,求证:1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa为定值.我不会打平方和四次方,只好搞成相乘了~我做的求证的那堆东东等于cosa.cosa+sinb.sinb.前面的推出:(sinacosb+cosasinb)(sinacosb-
已知sin(a+b)sin(a-b)=1/3,求证:1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa为定值.
我不会打平方和四次方,只好搞成相乘了~我做的求证的那堆东东等于cosa.cosa+sinb.sinb.前面的推出:(sinacosb+cosasinb)(sinacosb-cosasinb)=1/3
已知sin(a+b)sin(a-b)=1/3,求证:1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa为定值.我不会打平方和四次方,只好搞成相乘了~我做的求证的那堆东东等于cosa.cosa+sinb.sinb.前面的推出:(sinacosb+cosasinb)(sinacosb-
1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa
=sina^2*cosa^2+sinb^2+cosa^2*cosa^2
=cosa^2(sina^2+cosa^2)+sinb^2
=cosa^2+sinb^2
sin(a+b)sin(a-b)=1/3
(sinacosb+cosasinb)(sinacosb-cosasinb)=1/3
sina^2cosb^2-cosa^2sinb^2=1/3
(1-cosa^2)(1-sinb^2)-cosa^2sinb^2=1/3
[1+cosa^2sinb^2-(cosa^2+sinb^2)]-cosa^2sinb^2=1/3
1-(cosa^2+sinb^2)=1/3
cosa^2+sinb^2=2/3
所以1/4sin2a.sin2a+sinb.sinb+cosa.cosa.cosa.cosa=2/3(定值)