化简(sinα)^2*(sinβ)^2+(cosα)^2(cosβ)^2-1/2cos2αcos2β

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化简(sinα)^2*(sinβ)^2+(cosα)^2(cosβ)^2-1/2cos2αcos2β

化简(sinα)^2*(sinβ)^2+(cosα)^2(cosβ)^2-1/2cos2αcos2β
化简(sinα)^2*(sinβ)^2+(cosα)^2(cosβ)^2-1/2cos2αcos2β

化简(sinα)^2*(sinβ)^2+(cosα)^2(cosβ)^2-1/2cos2αcos2β
cos2αcos2β
=(cos²α-sin²α)(cos²β-sin²β)
=cos²αcos²β-cos²αsin²α-sin²αcos²β+sin²αsin²α
所以原式=(2cos²αcos²β+2sin²αsin²α-cos²αcos²β+cos²αsin²β+sin²αcos²β-sin²αsin²β)/2
=(cos²αcos²β+sin²αsin²β+cos²αsin²β+sin²αcos²β)/2
=(cos²α+sin²α)(sin²β+cos²β)/2
=1/2