求证sin²A+sin²B-sin²Asin²B+cos²Acos²B=1
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![求证sin²A+sin²B-sin²Asin²B+cos²Acos²B=1](/uploads/image/z/1241549-53-9.jpg?t=%E6%B1%82%E8%AF%81sin%26%23178%3BA%2Bsin%26%23178%3BB-sin%26%23178%3BAsin%26%23178%3BB%2Bcos%26%23178%3BAcos%26%23178%3BB%3D1)
求证sin²A+sin²B-sin²Asin²B+cos²Acos²B=1
求证sin²A+sin²B-sin²Asin²B+cos²Acos²B=1
求证sin²A+sin²B-sin²Asin²B+cos²Acos²B=1
证明:sin²A+sin²B-sin²Asin²B+cos²Acos²B
=sin²A(1-sin²B)+sin²B+cos²Acos²B
=sin²Acos²B+sin²B+cos²Acos²B
=(sin²A+cos²A)cos²B+sin²B
=cos²B+sin²B
=1
等式得证