求解三角函数

求证 sin^2 α+sin^2 β -sin^2 α*sin^2 β+cos^2 α *cos^2 β=1

sin^2 α+sin^2 β -sin^2 α*sin^2 β+cos^2 α *cos^2 β

=sin^2 α(1-sin^2 β)+1-cos^2 β+cos^2 α *cos^2 β

=sin^2 αcos^2 β+cos^2 α *cos^2 β)+1-cos^2 β

=cos^2 β(sin^2 α+cos^2 αcos^2 β

=cos^2 β+1-cos^2 β

=1

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