已知cos^4β/cos^2a+sin^4β/sin^2a=1,求证cos^4a/cos^2β+sin^4a/sin2^β=1

题目

已知cos^4β/cos^2a+sin^4β/sin^2a=1,求证cos^4a/cos^2β+sin^4a/sin2^β=1
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答案

证明：cos^4β/cos^2a+sin^4β/sin^2a=1cos^4βsin²α+sin^4βcos²α=cos²αsin²α(1-sin²β)cos²βsin²α+(1-cos²β)sin²βcos²α=cos²αsin²αcos&s...