化简sin²a+sinb²-sin²asin²b+cos²acos²b ,

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/29 17:26:33

化简sin²a+sinb²-sin²asin²b+cos²acos²b ,
化简sin²a+sinb²-sin²asin²b+cos²acos²b ,

化简sin²a+sinb²-sin²asin²b+cos²acos²b ,
sin²a + sin²b - sin²asin²b + cos²acos²b
= (sin²a - sin²asin²b) + sin²b + cos²acos²b
= sin²a(1 - sin²b) + sin²b + cos²acos²b
= sin²a cos²b + sin²b + cos²acos²b
= (sin²a cos²b + cos²acos²b) + sin²b
= cos²b(sin²a + cos²a ) + sin²b
= cos²b + sin²b
= 1

原式=sin2a+sinb2-sin2asin2b+cos2acos2b
=sin2a(1-sin2b)+cos2acos2b
=sin2acos2b+cos2acos2b
=cos2b(sin2a+cos2a)
=cos2b

sin²a+sinb²-sin²asin²b+cos²acos²b
=sin²a-sin²asin²b+sin²b+cos²acos²b
=sin²a(1-sinb²)+sin²b+cos²acos²b
...

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sin²a+sinb²-sin²asin²b+cos²acos²b
=sin²a-sin²asin²b+sin²b+cos²acos²b
=sin²a(1-sinb²)+sin²b+cos²acos²b
=sin²acos²b+sin²b+cos²acos²b
=sin²acos²b+cos²acos²b+sin²b
=cos²b(sin²a+cos²a)+sin²b
=cos²b+sin²b
=1

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