sin²a+sin²b-sina²sin²b+cos²cosb=1
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sin²a+sin²b-sina²sin²b+cos²cosb=1
![sin²a+sin²b-sina²sin²b+cos²cosb=1](/uploads/image/z/19392569-17-9.jpg?t=sin%26%23178%3Ba%2Bsin%26%23178%3Bb-sina%26%23178%3Bsin%26%23178%3Bb%2Bcos%26%23178%3Bcosb%3D1)
证明:sin²a+sin²b-sina²sin²b+cos²acos²b
= sin²a+sin²b-sina²sin²b+(1-sin²a)*(1-sin²b)
=sin²a+sin²b-sina²sin²b+1-sin²a-sin²b+sina²sin²b
=1
= sin²a+sin²b-sina²sin²b+(1-sin²a)*(1-sin²b)
=sin²a+sin²b-sina²sin²b+1-sin²a-sin²b+sina²sin²b
=1
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