◆◆◆求证sin^2a+sin^2β-sin^a*sin^2β+cos^2a*cos^2β=1
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◆◆◆求证sin^2a+sin^2β-sin^a*sin^2β+cos^2a*cos^2β=1
最好步骤简洁,能够让人明白,禁止抄袭!
应是sin^2a+sin^2β-sin^2a*sin^2β+cos^2a*cos^2β=1
最好步骤简洁,能够让人明白,禁止抄袭!
应是sin^2a+sin^2β-sin^2a*sin^2β+cos^2a*cos^2β=1
出错了吧?中间漏了个2?
sin^2a+sin^2β-sin^2a*sin^2β+cos^2a*cos^2β
=sin^2a-sin^2a*sin^2β+cos^2a*cos^2β+sin^2β
=sin^2a*cos^2β+cos^2a*cos^2β+sin^2β
=cos^2β*(sin^2a+cos^2a)+sin^2β
=cos^2β+sin^2β
=1
证完了.
sin^2a+sin^2β-sin^2a*sin^2β+cos^2a*cos^2β
=sin^2a-sin^2a*sin^2β+cos^2a*cos^2β+sin^2β
=sin^2a*cos^2β+cos^2a*cos^2β+sin^2β
=cos^2β*(sin^2a+cos^2a)+sin^2β
=cos^2β+sin^2β
=1
证完了.
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