化简sin^2acos^b-cos^2asin^2b+cos^a-cos^2b

来源:学生作业帮助网 编辑:六六作业网 时间:2024/05/14 08:25:38
化简sin^2acos^b-cos^2asin^2b+cos^a-cos^2b化简sin^2acos^b-cos^2asin^2b+cos^a-cos^2b化简sin^2acos^b-cos^2asi

化简sin^2acos^b-cos^2asin^2b+cos^a-cos^2b
化简sin^2acos^b-cos^2asin^2b+cos^a-cos^2b

化简sin^2acos^b-cos^2asin^2b+cos^a-cos^2b
sin^2acos^2b-cos^2asin^2b+cos^2a-cos^2b
=cos^2b(sin^2a-1)+cos^2a(1-sin^2b)
=cos^2acos^2b-cos^2acos^2b
=0

原式=cos²acos²b-cos²b+cos²a-cos²asin²b
=-cos²b(1-cos²a)+cos²a(1-sin²b)
=-cos²bsin²a+cos²acos²b
=cos²b(cos²a-sin²a)
=cos²bcos2a