已知sin(α+β)sin(α-β)=1/3求证1/4sin^2(2α)+sin^2β+cos^4α为定值
问题描述：
已知sin(α+β)sin(α-β)=1/3求证1/4sin^2(2α)+sin^2β+cos^4α为定值
答
1/4sin^2(2α)+sin^2β+cos^4α=1/4(2sinacosa)^2+sin^2β+cos^4α=sin^2acos^2a+sin^2β+cos^4α=cos^2a(sin^a+cos^2a)+sin^2β=sin^2β+cos^2a=(1-cos2β)/2+(cos2a-1)/2=1/2(cos2a-cos2β)=1/2*(-2)(sin(2a+2β)/...