cos^4a/(cos^2b)+sin^4a/(sin^2a)=1 求证cos^4b/(cos^2a)+sin^4a/(sin^2b)=1
问题描述：
cos^4a/(cos^2b)+sin^4a/(sin^2a)=1 求证cos^4b/(cos^2a)+sin^4a/(sin^2b)=1
答
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答
证明：输入过于麻烦,用换元法吧设A=sin²A,B=sin²B∵ sin^4a/sin^2b+cos^4a/cos^2b=1即A²/B+(1-A)²/(1-B)=1∴ A²(1-B)+(1-A)²B=B(1-B)∴ A²-A²B+B-2AB+A²B=B-B²∴...